If you simply don't believe in god, you're agnostic. If you actively believe that there is no god, you're atheist.
The burden of proof lies with the claim of existence. In the absence of any evidence, nonexistence is the default assumption. Yet disbelief in all of these things is based on evidence, since we have looked in the places people used to believe they lived and/or domains they were believed to control, andand they weren't there.
The universe either came from somewhere or has always existed... If I define God as a "the thing that created the universe" how would you prove or disprove God's existence?
...then you would have to justify that definition before expecting anyone to accept, prove, or disprove it.
FWIW I was once a believer and frequently associate with believers, so I have some experience in the matter and have given it considerable thought.
The point is I'm not talking about a specific God or assuming anything about the nature of God like many religions do. Once you remove all that baggage God is just a term that means "the thing that created the universe." So to deny the existence of God you must deny that the universe was created by something. I don't see how you can make such a claim without any evidence. Last I checked there was no scientific explanation for the creation of the universe.
It's an unnecessary complication; if calling the Big Bang or whatever might have preceded it "god" provides useful explanatory and predictive power, then such a definition might gain some traction. But as it is, the universe appears indistinguishable from a naturalistic physical process.
You can believe in a god (be a theist) and still think it's not provable that there is one (be an agnostic).