Thomas Aquinas put forward five arguments for the existence of god. Here are my responses to the first two:
1) "The Prime Mover" -why does god get to be an exception? If you truly believe that everything that moves was first moved by something else, then who moved god? Why does he get to be a special situation? It is as arbitrary as if we declared that the Big Bang is the Prime Mover, that was not moved itself. You will no doubt object to that as I object to arbitrtarily claiming that there is this special being that has the ability to not have been moved itself. Where is the proof that such a being exists? The original problem remains for both of us, meaning that we don't know how things played out in the distant past, but Thomas's "solution" only gives the illusion that he has solved the problem, it is not a solution at all, for he has to explain how it is that he can have a prime mover that violates his basic argument that everything that moves has to have something that put it in motion. There is no good reason to make an exception to that rule and call it god.
2) "The First Cause" - see above, as my refutation is the same except first cause would be substituted for prime mover. Who caused god? If you claim no one did, how can you justify making an exception, when there is no independent way to verify that such a non-natural being exists.
More fundamentally, why can we not have an infinite past? Why cannot motion be the status quo? Then we don't have to explain where it came from because it just always has been. See the thing is we only have to explain the first movement if things were originally static and motionless and then things started to move. But, if movement has always been, then it needs no explanation.
"Beginning" is just a frame of mind and is always relative to something. As difficult as it is to imagine, there does not have to be a beginning of all beginnings. If you disagree, prove why there must be a beginning. You will not be able to do it (Aquinas's arguments based on assumptions do not do it). If you can believe in an eteranl god, you can believe in an eternal cosmos (including what came before the Big Bang). If you can believe in a beginningless god, you can believe in a beginningless cosmos. We have never observed a beginning (an ultimate beginning - a beginning that comes from nowhere), why do we assume that such a real beginning even exists at all?