actually its pretty easy for the republic / empire to raise an army of non clone troopers, the original idea was that the emporer came into power using pro human anti alien propeganda to gain support.
humans are found in almost every corner of the galaxy, so it wouldnt be hard to get a bucnha humans riled up and wanting to join the army by saying aliens are attacking or bombing human settlements, but in reality Lucas never intended the stormtroopers to be clones, and he has even admitted this.

origianlly the stormtroopers were going to be left overs of the mercenary army of manderlorians, then he changed the idea to let the mandalorians have been killed off by the jedi but basicly also wiped out most of the jedi, and boba fett was supposed to be the last remaining mandalorian.

however things of course continued to get changed, and lucas scrapped alot of his older ideas thinking his newer ones were cooler, for instance in the original story of a new hope lucas intedned there to be a wookie battle but since he couldnt do it he attempted to mimick it in return of the jedi, with the ewoks. now in episode 3 he is again going to attempt to do it with actual wookies, (interesting side note EWOK is derived from the word WOOKIE) so while now the story has been changed to make storm troopers clones i think that it doesnt neccesarrily mean we have to accept it, perhaps they intermixed clones with recruits from the imperial acadamy, i think at this point since there are so many difrent versions, you can take and pick and choose what you like.

I mean lucas screwed so much stuff up now hes trying to even fix some things like erasing the greedo shoots first, or having han step on jabbas tail.