We may also consider that Zephram Cochrane of Alpha Centauri was considered to have "discovered the space warp", probably sometime in the 21st century but at least before his disappearance in the 2110s, according to TOS "Metamorphosis".
It might in theory be that no species in the universe known to our TOS heroes had discovered space warp prior to Cochrane, and that everybody we saw warping in ENT had acquired that capability after 2063. At least that was probably the intent of the writer of "Metamorphosis", and so far only a single piece of canonical evidence seems to go directly against this idea: the presence of a "warp engineer" aboard a Vulcan ship in 1957 in "Carbon Creek". Apart from that, all our alien references are to interstellar travel by unknown means, not to warp drive as such.
In practice, though, no recent writer of Trek has considered Cochrane to have been the inventor of warp drive in the general sense - but merely in the sense of introducing that drive to the human species on Earth. Supposedly, other species had their own Cochranes, or bought or stole warp from yet other species. It's just that the evidence isn't explicit, and a stubborn arguer could still support the claim that humans were the first (out of the usual players at least) to come up with a working warp drive, in 2063.