While the story the Futurians was a fiction they told to manipulate Japan, they sparked events that lead to that very future becoming reality. Most of the events we see take place in this timeline are prior to the divergence point between it and the VS-3 timeline. The only part of Godzilla vs. King Ghidorah that exclusively occur in this timeline are the scenes in 2204, when the EUO sub discovers the now two-headed body of King Ghidorah. Although this is more than the VS-1 timeline, we actually know less about this future because it isn't the one Emmy is from. The Futurians who visit 1992 are, remember, from the VS-1 future, the VS-2 future that Emmy travels to isn't her world anymore. Some things are clearly the same, the EUO still exists, she has allies in that time who seem to know her, and she has the ability to get the Mecha-King Ghidorah project going, so the Emmy of the VS-2 2204 must exist and have some sort of presence in the world. Which I think means the VS-1 Emmy stole the VS-2 Emmy's identity? That's assuming the Futurians were lying about not being able to have two of the same person in the same place at the same time, of course, which they absolutely were. Either way, this timeline is the shortest because it has the least amount of information and the most questions.
Key
Superscript = These are the number of the film in the series where the information comes from, with 1 being Godzilla, 2 being Godzilla Raids Again, etc. Additional superscripts will indicate supplementary sources not present in the films themselves, which will be explained at the bottom of the page.
Bold = Below the year heading, dates and times in bold are ones that taken directly from the films. These are anchoring points used to figure out when the rest of the events take place.
Alert Level 1: Issued when any scientific, geological, meteorological, or psychological evidence, except for the physical evidence, of G's activity has been confirmed.
Alert Level 2: Issued with G's physical activity, such as voice and movement, has been confirmed.
Alert Level 3: Issued when G has appeared.
Alert Level 4: Issued when G would certainly land on a specific site in Japan.
1992
July 1st, 18:36 to 19:01 - The 23rd century time machine MOTHER arrives from the year 2204 and is spotted over the skies of Tokyo.18
19:01 to 19:25 - MOTHER turns and heads towards Mt. Fuji, where it lands.18
19:25 to 23:59 - KIDS launches from MOTHER and flies over Godzilla in the sea of Japan to analyze him and determine the possibility that the hypothesis from the book The Birth of Godzilla about Godzilla's origin is correct. The result is a 98% certainty.18
July 2nd - The writer Kenichiro Terasawa interviews a World War II veteran who's been causing a scene at the Dinosaur World attraction, who claims that while stationed on Lagos Island during the war, him and his garrison were saved by a dinosaur that attacked the US forces.18
July 3rd - Terasawa conducts another interview with Professor Hironori Mazaki, who is a complete kook that thinks birds aren't dinosaurs and the basking shark skeleton dredged up by the Zuiyo Maru was a plesiosaur. That night, MOTHER destroys two helicopters.18
July 4th, 10:00 - MOTHER broadcasts a message to the JSDF stationed around it requesting a meeting in 3 hours.18
11:30 - Tersawa interviews Yasuaki Shindo, chairman of the Teiyo Group, about his experiences on Lagos Island during the war. He initially denies knowing anything about the dinosaur, but shares a few photos after being told the hypothesis that it became Godzilla.18
13:00 - The three human inhabitants of MOTHER, Wilson, Glenchico, and Emmy Kano, reveal themselves as people from the 23rd century, and request a meeting with the Prime Minister tomorrow at the same time.18
July 5th, 13:00 - The Futurians teleport into the Prime Minister's office and tell the cabinet that by their time, Japan has been rendered uninhabitable by Godzilla. They produce an antique copy of the book The Birth of Godzilla and present its hypothesis before the book is even finished. They ask to bring Miki, Terasawa, and Professor Mazaki with them to 1944 to identify the dinosaur as Godzilla, and teleport him away from the island, therefore erasing Godzilla from history.18
13:00 to 20:00 - Miki has a psychic vision of Godzilla moving as he swims from the Sea of Japan to the Bering Sea.18
20:00 - Terasawa and Professor Mazaki are summoned late that night and informed of the Futurian's plans, and Terasawa examines the aging book from the future that he is still working on in the present.18
July 6th, 14:30 - The three civilians are transported to MOTHER and board the time ship KIDS along with Emmy Kano, M11, and a trio of Dorats. They travel back to 21:00 on February 6th, 1944.18
July 6th, 15:00 - KIDS returns from 18:30 on February 14th, 1944. Godzilla does seem to have disappeared from his previous location, but in his place a new monster, King Ghidorah, appears.18
15:00 to 20:00 - King Ghidorah rampages through Kyushu, attacking Fukuoka and Hiroshima among other cities. Miki theorizes based on the monster's appearance and what she witnessed during her time trip that Ghidorah was created deliberately by leaving the Dorats behind on the island in order to use their empathic powers as a way for the Futurians to remotely control the monster. The Futurians, having caused enough damage in Kyushu, send King Ghidorah north to Hokkaido.18
20:00 - Emmy, unhappy with the way their monster is being utilized, sneaks out of MOTHER and reveals the truth about the history of the future she's from, as well as the true intentions of coming back to this time.18
July 7th - Wilson and Glenchico issue an ultimatum to the Japanese government, but instead a new plan is developed to fight King Ghidorah under the pretense that Godzilla really has been erased from history (despite the fact that everyone remembers him). They plan to intentionally mutate the Godzillasaurus in the Bering Sea into a new Godzilla. To this end, Shindo of the Teiyo Group reveals the existence of the Musashi No. 2, a sub carrying torpedos filled with nuclear waste stationed in the waters of southeast Asia. Miki has another psychic vision, and insists she's seeing Godzilla, not the dinosaur.18
July 8th - In the archives, Terasawa's assistant Chiaki digs up an article about a nuclear sub sinking in the Bering Sea. Later, Miki confirms through satellite imaging that Godzilla, not an unmutated Godzillasaurus, is in the Bering Sea. Terasawa and Emmy attempt to warn people that Godzilla still exists and the Musashi No. 2 is sailing to its doom, but are chased down by M11, who takes Emmy back to MOTHER. That night, Godzilla does destroy the Musashi No. 2. Emmy reprograms M11 and sends him out to get Terasawa.18
July 9th, 14:00 to 14:11 - Godzilla surfaces in Abishiri, now even larger than before after the additional consumption of modern nuclear waste. Wilson orders King Ghidorah to be sent to attack Godzilla, and the two battle, with Ghidorah seeming to get the upper hand.18
14:11 to 14:16 - Emmy, Terasawa, and M11 sabotage MOTHER's computer, causing the backup countdown to start, which will return the ship to 2204 in 20 minutes. It also causes Ghidorah to go out of control, giving Godzilla an edge in the battle.18
14:16 to 14:21 - The three confront Wilson and Glenchico. After a brief fight, they knock out the two and scramble to KIDS.18
14:21 to 14:30 - Godzilla blows off Ghidorah's middle head with a blast of his atomic beam. KIDS teleports MOTHER to Abishiri, right in front of Godzilla.18
14:30 to 14:31 - Godzilla destroys MOTHER with a single blast just as Wilson and Glenchico regain consciousness, then turns to the fleeing Ghidorah and blows a hole through one of its wings. Ghidorah flies out to sea but collapses and falls into the Sea of Okhotsk.18
18:46 - An evacuation order is given for Sapporo as Godzilla nears the city.18
19:00 - Godzilla rampages through Sapporo and crushes a defensive line of MBT-MB92 maser cannons.18
19:00 to 23:59 - Terasawa comes up with the idea to revive King Ghidorah as a cyborg with 23rd century technology and time travel back to 1992 in order to defeat Godzilla. Emmy agrees to the plan, and boards KIDS with M11 and travels to 2204.18
July 10th - Godzilla destroys Shinjuku, which includes the headquarters of the Teiyo Group, killing Shindo in the process.18
July 11th to December 31st - Godzilla continues to rampage across Japan, with all attempts to stop him failing.18
1993-2001
The damage done by Godzilla, as well as the radioactive contamination of Japan resulting from his rampages, force the Japanese people to abandon the archipelago, and Japan as a country ceases to exist. The destruction of the second largest economy in the world due to the overreach of private enterprise becomes an important cautionary tale in history.18
2001-2100
The United Nations gives way to a new international body, the Earth Union Organization.18
2204
Emmy travels into a new future where Godzilla has destroyed Japan just as in the fake story she and the other Futurians gave to the people of 1992. With the help of M11 and the EUO member Morrys, she locates the still living body of King Ghidorah in the Sea of Okhotsk, and Morrys agrees to help her revive the monster as a cyborg, and bring it back to the 20th century to give Japan a brighter future.18
Sources
18 - Godzilla vs. King Ghidorah. This movie has a lot of visible dates and times, unsurprisingly for a time travel movie. The cold open is 2204, and then we're told its 1992, and a few scenes after that we're shown the path of MOTHER from 18:36 to 19:25 on the night of July 1st. Now I've used the technique for these timelines of "counting days" before, basically looking at the time of day of each of the scenes and counting each time a new day begins. Here the practice is validated, because if you count the number of days that pass in this way since the night of MOTHER's arrival in 1992 up to the computer screens onboard KIDS before they travel to 1944, you'll see reads July 6th, which is exactly consistent with what we're shown and told about how much time has passed in the film.
A summary of the rest of the times is as follows: We're told the Futurian's message is recieved at 10:00, and the messages asks for a meeting at 13:00, where they ask for a meeting with the Prime Minister the following day at the same time. We know this happens on the 4th and 5th because when our ensemble travels to the past the KIDS computer puts the present as 14:30 on July 6th, 1992, with the destination time as 21:00 on February 6th, 1944. We can see KIDS time travels again but we don't see the computer until the teleportation sequence, which has both the current and destination time as 18:00 on February 14th, 1944. This suggests that KIDS can teleport things to different destination times, making time travel and teleportation technology virtually indistinguishable. When they return to 1992, the present says 18:30 on the same day with the destination as 15:00 on July 6th, 30 minutes after they left. After this we don't get anymore clearly legible dates, which is frustrating. Miki says after her vision of Godzilla the day after her time travel trip that she last had one two days ago. We know that MOTHER's back up return trip is on a countdown of 20 minutes and Godzilla destroys it when that countdown is at t minus 1 minute. We also can see the times on the Sapporo TV tower, which confusingly uses a 12 hour clock because apparently everyone in Sapporo is a dark age heathen demon that hates common sense. It is 18:46 when everyone is ordered to evacuate and 19:00 when he destroys the tower. Taking Godzilla's maximum land speed of 60km/h according to various promotional materials and the like, it would have taken him 4 hours, 28 minutes, and 49 seconds to clear the 260.82km between the coast of Abashiri and the Sapporo TV tower, and a further 13 hours to go the remaining 830.85km from Sapporo to the new Tokyo metropolitan government building.
During the meeting about the UFO, Miki states that Godzilla has been out at sea for over 1,000 days. This isn't... uh... possible. 1,000 days before July 2nd, 1992 would be October 6th, 1989. Godzilla vs. Biollante gives us three objective, written dates: the "5 years later" intertitle, the 1985 of the Godzilla memorial lounge, and the envelope prop which has 1990 on it. The envelope's date isn't visible in the film, we only know it says 1990 because of a photo in the Godzilla Heisei Perfection book, but the 1985 is, and that clearly says that's when Godzilla appeared. In case you missed remedial math, 1985 + 5 = 1990. In addition, the fact that based on my calculations the first scene in 1990 in Biollante occurs 5 years to the day after Erika's death is really, really difficult to handwave because Miki gave a vague, rounded number. So I'm going with the dates that are written down, and if you don't like that, feel free to make your own timeline where you can justify how Biollante happened in January. And for the record, July 2nd, 1992 is 698 days after August 4th, 1990.
