We've never really been told "Species X achieved warp in year Y". Instead, we've been shown that humans on Earth first achieved (manned?) warp drive in 2063, and that numerous species had warp drive in the 2150s when the show ENT took place.
Major or familiar species that had warp in ENT:
Klingons (no mention how long they had had it)
Vulcans (again no mention, but a ship of theirs had a "warp engineer" aboard in 1957 already)
Romulans (again no mention)
Andorians (again no mention)
Tellarites (again no mention)
Ferengi (again no mention)
Borg (again... you get the picture)
If you take trek lit into account:
The klingons obtained warp drive from the Hurq, invaders who once conquered the klingon world, then a medieval society, not only socially, but also technologically.
The vulcans/romuland did not have warp drive when the romulans went in their exodus. The romulan journey was made in relativistic, near-light-speed ships.
The borg had warp drive from the moment they were born in their current state - being 'descendants' of warp-capable species.