Is there a generation of games, where you could theoretically

Gen III, pre-FRLG, was the only point in the series during which you could not catch them all.

Aside from that, generally almost all Pokemon have been available each gen.

>>25697346
Checked it, you seem to be able to get all Pokémon but mew, lugia, ho-oh, celebi and deoxys in gen 3.
Looks like a decent Challenge

>>25698679
>not Jirachi
If you're gonna include Gamecube stuff, Lugia and Ho-oh are perfectly obtainable.

>>25697346
Pretty much the whole of Gen II wasn't available in Gen III

>>25698762
Pretty much every gen 2 Pokemon was available in Emerald. The starters were hilariously impractical to get a full set of, though (one per file and you had to complete the Hoenn Pokedex to claim it).

You almost need the gamecube games to pull it off.