When Eren wakes up from his dream in first episode, in the Manga, Mikasa said "See you Later, Eren" and out of blue, he asks her if her hair has gotten longer. This, first of many forshadowing that the author throws at us might give us some insight. My theory is that 2000 years from now, in about 2800, the world is still the same. SnK's world is inspired by the Viking mythology, as shown in many references throughout the story and names of certain characters. For instance, Armin talks about the outside world; Sea of flames and Field of Ice. Which, if you look for it in the Norse(viking) Mythology, it exist the outside of Midgard and Jötunheimr - a fucking world of giant. Sea of flames is called Muspelheim, and Field of ice (plane of ice?) is called Niflheim In Norse Mythology, they build a wall against the giants. with the eyelash of Ymir - incidently a name of a character in the SnK. When Ragnarok happens in Norse Mythology, those giants break down the wall and kill the gods...basically, SnK. Ymir is the primeval being, the very first being in the Norse Mythology whom of which killed by Odin and other major gods. In death, Ymir's body create the world. Gods try to protect themselves and humans from the giants by making the wall. This is the part of Norse Mythology SnK uses.
Back to SnK, world creation is probably similar to the Norse Mythology. Ymir - some primeval being - was killed and remnant of it was scattered across the world. In year 700, the remnant was found by a young scientist (Eren's father.) He experimented on it, and extracted a virus to titan-fy things. Some plants that he experimented on create the gigantic forest outside the walls of SnK. The nation start to investigate on the Remnant of Ymir and create the Titans. The nation decide to use the Titans as a part of their conquest. "The world without conflicts" (On the cover of a second book, the map has upside down writing that reads that) It was simple, they build the walls to protect themselves safely inside, and spread the giants outside to devastate everyone else. They probably had some sort of vaccine that will kill Titans. From the beginning, I was wondering how the walls were conveniently built once Titans appeared. Walls were under construction by the royalties in secrecy, and when they released the Titans, they just lead the survivors and escape into the pre-built walls. The plan was wait it out until the titans outside devastate the other nations - they are only interested in killing human - and kill the titans by spreading the vaccine. All this project, for the convenience, I will call it Ragnarok Project.
However, they needed a messenger. sort of a like a bird in Noah's Ark. They needed to know when they can come out. So they created Titans with intelligence and who can become human at will. They created those straints of titans, however they only had vaccines to eliminate titans - in which will kill the messenger titans also.
In short, there's two kinds of titans. ones that were created initially, one without any intelligence of sort and no way of going back to Human. And another one that can become human at will.
The plan was perfect, the speed of devastation was unimaginable. However, they evolved. Some of them gained intelligence. They now have their own agenda - to create the world of giants. Titans with intellignce tried and succeed in killing the scientist and the vaccine.
Those messenger titans - one that can revert back to human - create their own nation outside the walls. If needed, they can change back to titan form, so the protection is ok. Reiner and Bertolt told Eren of where they came from - outside of wall. Well, they were revealed to be titans in manga.
To clarify, there's 5 major powers in this world now.
Humans and royalties who created Titans (Midgard, Asgard)
Titans without intelligence
Titans with Intelligence (Jötunheimr)
Messenger Titans who joined Jötunheimr. (Ymir)
Messenger Titans who created their own nation. (Reiner, Bertolt, Annie)
Anywho, the scientist had a son, Eren, who had the vaccine. However, Eren didn't know or didn't have guts to use the vaccine. In order to do so, he will have to come forward with the vaccine and expose himself. He hid it in the lab of his father and waited till he can use the vaccine. However, in 850's, he was killed by Titans and the vaccine and the location of the lab is lost. The Ragnarok Project that began in 700s, is continuing without any way of ending it. This state of entrapment of human continues for 2000 years. And by then, almost all titans have intelligence. However, the world is already theirs, and they saw no reason to breach the final wall. Those royalties and survivors tried to come up with a way to kill Titans. Due to the constraint of the wall, humanity was unable to build any substantial weaponary against the titans. Also, they failed to produce the vaccine again since they were unable to capture the titans in any shape or form and also, anyone who gets close to the answer gets killed by the titans. Finally, the vaccine and the virus are both created from the remnant of Ymir, which discovered in 700, only the scientist who discover can know of it back then, so in year 2700s, they can't figure it out. However science advanced regardless. They gathered as much resources as possible in a hope that one day they might come up with a plan.
At one point in history, they find a letter - "To you, 2000 years from now." Written by Eren in 850's. This letter, explained the plan that humanity is going to do. They create the time machine with all the resources and scientific advances combined. The purpose of the time machine is to send assassin into 700s to kill the Eren's father before he create the Titan virus. However, for some unknownreason this fails, and the future fails to change. In year 2800, the titans attacks human one last time and humanity comes to an end.
At the year 2800s, the descendant of Mikasa send her son, Eren, back to the past in a hope to save him from the Titans. She sends him off with her final word "See you later, Eren." It is impossible even for her son, Eren's eye. This is why he cries when he wakes up. I assume that Mikasa's name was passed down to her descendents. Since she is...quite obsessive of Eren, she probably wished that the son of her lineage will be called Eren, and daughter Mikasa. However in time warp, only the memory warp back.
Due to the nature of the travel, the original Eren's memory and 2800's Eren's memory collide with one another, and he only feels as if he was dreaming. However, since Mikasa's lineage is quite unique (Oriental) future Eren's mother, Mikasa, is similar enough to past Eren's Mikasa. I guess the future one had short hair, that's why he asks her about the hair when he wakes up.
Eren's father, the shots that he gave to Eren, was to protect Eren from the danger of Titans. He made it so that Eren will be like Messenger Titans. Also, he disrupts Eren's memory of location of his lab and what is in there (most likely vaccine)
In 850's, Eren's memory finally collides, he realizes the fate of humanity in the future. He hurries to the lab only to realize it is already ransacked. He was already surrounded by titans. knowing that there's no way out, he writes to the future that he came from the future and back to 800s, but he failed, so that future humans should send assassin to year 700 instead to kill his father instead. This is the letter, "To you, 2000 years later"
In future, the letter is found. In year 2800, they send assassin back in 700s, and failed. In the brink of extinction of humanity, Mikasa send her son, Eren, back in time just to save him. The loop continues on.
Back to the Norse Mythology, after killing gods, the titans set the world on fire. However, the fire is not for the destroying, it is for cleansing the world.
In SnK, this could mean that the titans are the bringer of the new future, the cleanser of the world instead of mindless devastation.. but this might be too hopeful.
TL;DR
The SnK's world is in Time loop without the possibility of multiverse. In the end, the humanity is extinct.
In 700s, the scientist finds the Remnant of Ymir (the primeval being) and create the virus. The royalty of current nation in SnK weaponize them by creating Titans and Messenger titans that will tell the end of devastaion outside the wall. However, they lose the vaccine that will eliminate Titans. Only ones that know the whereabouts of the vaccine is Eren and his father. However when Eren finally reaches the lab, lab is ransacked (probably by intelligent titans) and Eren is killed
Eren, knowing the truth about him writes the letter, "To you, 2000 years from now," before his death that soon follows. In the future, when humanity find the letter, they realize the possibility of time travel and create time machine. They send back the assassin into 700s to kill the Scientist, but fails. Titans are created. In 2800s, Mikasa sends her son, Eren, back to the past to save him from the Titans and the history repeats itself. The loop is completed, and even with the Time machine, the humanity meets its extinction.