A simple challenge for atheists

[Esquilax]

My impression is that the consensus among cosmologists is that our universe is not infinite in the past so you must be saying that the universe (time and space) could have popped into existence uncaused?

There's a subtlety to the finite universe positions that theists often miss, even in the theorems that creationists use as evidence for their position, which is why cosmologists don't think the universe was past infinite: at a certain point in those models our normative understanding of causation breaks down. Essentially, there's a point on the graph past which we're unable to accurately predict what goes on, and that is the point at which our linear understanding of time stops being a thing. This is why, even if you read the work of cosmologists who advocate for a past-finite universe, you'll see at least one passage detailing this, along with an admission of ignorance regarding what goes on beyond that point. It's not the "universe must have a cause," case that you think it is.

There is no special pleading and nothing was excluded in the argument. Perhaps I should have spelled it out: Everything that begins to exist has a cause, the universe began to exist, therefore the universe has a cause.

"Begins to exist" is the special pleading: you're asserting one category for everything else, and a special category exempt from the rules for your god, and providing no evidence for the existence of the latter category. In that way, it's also kind of begging the question.