You could always do a Nuzlocke-style approach (but cut out the death rule and the other minor rules) and only use the first Pokémon you find on each route, skip over duplicates, and just pick and choose from the Pokémon you end up getting.
You could also just do a random Pokémon generator thing using
this site.
Or, you could do a Scramble Challenge type of run, where you ask for people to give you Pokémon. Most of the time people add special conditions, too (e.g. can't evolve, must learn X move, can't evolve until level X), but if you wanted regular Pokémon you can just ask for people to give you Pokémon and ask for no special rules like that. If you're looking to do that, you can bump
this thread and ask there, as it's probably the most efficient way to do it rather than creating a new thread just for that or using the Q&A thread where it might clutter up with multiple people giving you a Pokémon.
Those are my suggestions, anyway. Hope they help.