Kaebora Gaebora is an ancient sage, we have no idea how old he is at the time of OoT or how long he can stay around.

PH shows Gorons thriving in the Great Sea

Zoras are mentioned by name in PH as well

Dodongos are shown in LoZ (i believe in WW-PH-LoZ-AoL-OoX-TMC-FS-FSA)

Deku Scrubs are in other games (like in OoX and maybe even TMC-FS i cant remember) that i believe to be post-flood, they are more monsters than a race anyway, to explain them youd have to explain several other races of monsters that constantly reappear, also they say in FSA that they love dark areas, thats why they live in the shade of the Lost Woods, so they give their reason for being there.

EDIT: PH also has many Gerudo-esque characters whose race is never specified but who act alot like Gerudos.

Its not illogical if an Island Hyrule is strung together by the Deku Trees, that all of the survivors from these races moved on home and eventually began to thrive and civilize again.

EDIT2: if you have more evidence, please continue.