[Pursuivant]

Because TOS was produced in the mid 1960s, the writers made some very optimistic projections about how quickly humanity could move into space. Later episodes postulated that there were nuclear wars on Earth in the 1990s, but at the same time there were STL ships which were capable of interstellar travel and reliable if somewhat immature "cold-sleep" technology.

The only way to reconcile our timeline and the Star Trek prime universe timeline is to assume that ST takes place in an alternate universe from our own.

Due to interventions by ancient aliens and time travelers from the future, human history in the ST universe is very close to our own history until about 1965. After that, humanity develops interplanetary space travel at a much faster rate than we do in our timeline. Due to the presence of the Augments, there is greater overall technical progress, but also much more serious wars in Eurasia, including nuclear exchanges. Possibly the US and Western Europe manage to stay neutral during these wars. The USSR never breaks up (or, at least, Leningrad isn't renamed St. Petersburg in the 1990s).

Prince Charon's timeline is reasonable for one of the myriad ST alternate universes, but slows human technological development down by about a century.

Canonically:

* Various coalitions of Augmented Humans taking control of much of the world by the late 1980s or 1990s. This implies that a number of augments were born in the 1950s to 1970s, which might imply the existence of ultratech (TL9+) genetic engineering technology prior to that time.

* Robust STL interstellar space travel exists by the 1990s. STL exploration of the Sol system begins.

* In the 1990s, conventional and nuclar wars which kill millions are instigated by augment rulers, notably Khan Noonien Singh. The surviving citizens of the affected nations revolt, forcing the Augments to flee Earth. Earth quarantines the remaining Augment embryos, keeping them in cyrogenic stasis. Laws are enacted which restrict genetic manipulation of humans to just correcting genetic defects.

* Between the 1990s and the mid-21st century, numerous interstellar colonization ships leave Earth for various alien planets. Many of these ships, or the colonies they founded, are lost. Starfleet periodically discovers surviving isolated human colonies until the late 24th century.

* By 2024, social conditions in the US had badly deteriorated, to the point that poorer people were confined to walled ghetto areas. Things only improved after the Bell Riots of 2024.

* At some point in the 21st century, the colony of New Berlin is founded on the moon.

* Sometime after 2050, a permanent colony is established on Mars.

* In 2053, a severe nuclear war devastates much of the planet, setting up the social conditions necessary for a united Earth government.

* In 2063, Zephraim Cochrane achieves Warp I travel. The crew of the Vulcan ship T'Plana Hath immediately makes first contact with humanity.

* From 2063 to 2151, the Vulcans assume the unofficial role of "senior partners" in guiding humanity towards a higher moral and intellectual state while also restricting human access to state of the art interstellar technology. Humans starships are typically limited to Warp 2. Sometime in this period, the United Earth Cargo Service, consisting of a number of freighters, is established to link Earth with other warp-capable species.

* In 2151, United Earth Starfleet finally completes the first warp 5 capable starship, NX-01 USS Enterprise. Humanity begins to explore the Alpha Quadrant, eventually becoming an important unifying force in the region.

* In 2153, at least some timelines, a species from an alternate plane of existence, known only as the Sphere Builders, convinces the 5 species of Xindi Alliance to attack Earth.

* In 2154, Romulan plots to foment war between the Andorians, Humans, Tellarites, and Vulcans backfire badly, leading the four species to create a loose self-defense coalition.

* In 2163, the United Federation of Planets is established in San Francisco, Earth. The Andorians, Humans, Tellarites, and Vulcans are the initial members.

For ST obsessives, the Memory Alpha fan site is probably the best source available for canon material. They have timelines that are far more detailed.