While I don't think the universe is deterministic, the existence of evolution isn't proof of this. It's possible that what we perceive as "randomness" is actually just the result of variables and things happening that we're not able to perceive.
Take rolling a dice: which number comes up is determined by the starting conditions, the force you throw it with, what it lands on and any external forces acting during the throw. It's not random at all, just hard to predict.
Well you can't conflate the banality of rolling dice with evolution. Based on what I've read, randomness has been a necessity for it's fruition, but of course this isn't my field.
My point was we call both “random” but, when you think deeply about it, you know that rolling a dice isn’t really random, we just can’t reliably predict the outcome.
There’s no reason the “random chance” in evolution is any different. It can just contain a million times more complexity in its determinism.
To prove determinism one way or another, we need to prove the fundamental building blocks of the universe are deterministic (or not).
Take rolling a dice: which number comes up is determined by the starting conditions, the force you throw it with, what it lands on and any external forces acting during the throw. It's not random at all, just hard to predict.