I would like to outline the basic branches of the argument:
Some theists may like to say "The universe cannot have come into existence itself, it must have a creator".
A non-theist might then say "Doesn't the creator then also need a creator?"
The theist may say one of two things: "No, the creator can just spontaneously come into existence" or "No, the creator has always existed."
With either of those answers, a non-theist would then say "If you allow for the possibility that the creator could do that, then it seems equally reasonable for me to allow for the possibility that our universe did that itself without a creator".
Here's a wikipedia page on the question, including quotes from both sides of the debate:
https://en.wikipedia.org/wiki/Problem_of_the_creator_of_God
This is one of those questions in philosophy, like many, that is perennially unsettled formally, and how you choose to resolve the debate comes down, apparently, to personal intuition. Some people seem to intuitively feel like "God can create itself, or have always existed, but the universe cannot". Other people intuitively feel like God, as a complex thinking being, must be in some sense complex enough to say "if the universe needs a creator, God does too".
The wikipedia page lists many counter-arguments from theists, mainly, so allow me to post a couple alternative links.
Stephen Hawking has some thoughts on the matter.
This is a debate, as you can see, that's been going on for many decades (centuries?), and it hasn't stopped yet. I may have my own opinion and my own intuition, but I wouldn't say that people who disagree with my thoughts are necessarily making obvious grave errors in reasoning. It's a tricky one.