I had a solid surface bathroom vanity top that didn't have holes
either. I got
a mansonry drill bit. Wasn't corian, but by transolid.

You should be able to drill smaller holes but you must make sure it is
even. The oversided holes makes sure the faucet isn't crooked. Also,
don't force in the supply lines from the faucet, they will kink.

My biggest problem was starting the hole. The drill bit would move off
the mark before it made an indent. I recommend having a shop vac going
because it make quite a mess.

c_kubie