When normal people talk about "the universe," they mean stuff: matter, energy, and all that. When physicists talk about "the universe," they mean the spacetime continuum, the container for all the stuff.
This is important to understand because when physicists talk about the Big Bang and the beginning of the universe, they're talking about the beginning of spacetime, but many normal people think they're talking about the beginning of the stuff in the universe. This causes confusion, particularly when it comes to discussions about the Cosmological argument.
From here, we run into a problem with human language. Language comes with certain underlying assumptions that we don't realize we are making. For example, most of the words in the English language assume that space and time exist simply because the idea of them not existing did not come about until recently when humanity had proof that spacetime is expanding as predicted by Einstein's equations. The idea of not-space or not-time simply do not exist as underlying assumptions anywhere in the English language, and so naturally, we have a difficult time talking about those things. Since we think in words, if we have difficulty even describing such a thing, we're going to have a difficult time thinking about it as well.
Words like "cause" and "exist" assume the existence of space and time.
If I tell you "I am outside the shed," I am assuming that space exists at the shed, at me, and in between myself and the shed. But what if space only exists at the shed, but not at me nor in between myself and the shed? What does the statement "I am outside the shed" mean then? Unfortunately, in this case, the statement becomes utterly nonsensical because the words "am" and "outside" are meaningless without space.
Can the Universe Have a Cause?
We run into similar problems with "outside of time" or "before time." If I tell you that A causes B, language inherently assumes that time exists at A, at B, and in between A and B.
When we talk about the universe having a cause, we run into a problem because "the universe" is spacetime itself. In other words, we are saying "A causes B" when time exists only at B, but not at A nor in between A and B. We can't say A causes B if B is time itself.
This is where cosmological arguments for the existence of gods fall apart, and this is the reason William Lane Craig is desperately trying to disprove Einstein's Relativity in order to salvage his version of the Kalam argument.
Doesn't Science Claim the Universe Has a Cause?
Not currently. There are a number of hypotheses that posit other spacetime continuums in order to allow for the creation of the universe, but since we cannot meaningfully interact with anything outside of our spacetime continuum, we cannot at the moment prove any of those hypotheses.
For example, the Holographic principle posits that our four-dimensional universe (3 dimensions of space, one dimension of time) is actually a four-dimensional projection of a two-dimensional surface which is the event horizon around a black hole in another universe. The math checks out, but at the moment there's not any way to prove it. Besides, the problem it was created to solve was solved by other means, so it kind of got moved to the back burner.
Anyway, if we posit that the Holographic principle is true, then from the point of view of people in that other universe, our universe has a cause. It was caused by whatever caused the formation of that black hole. However, from our point of view, the universe appears to be uncaused because we cannot meaningfully detect nor prove anything about the cause, nor meaningfully interact with anything in that other spacetime continuum.
So yes, it's technically possible that the universe has a cause from a certain point of view, but for now, such things are entirely unproven, and it may be that we will never be able to prove any such thing. At the moment, we are limited to talking about this spacetime continuum.
Other Problems with "Outside of Time"
Because of the problems with the cosmological arguments, many theists claim that their god exists outside of space and/or outside of time. William Lane Craig takes it one step further and claims that his god is "timeless."
Again, we run into problems. What does a word like "exist" even mean without time?
As TMM of YouTube has pointed out (forgive me, but I don't recall which specific video or I would have provided a link), if God exists without time, then by definition He cannot be sentient, since having thoughts necessarily involves a change in mental states over time. If God is timeless, then God is a brainless natural force incapable of having a meaningful cause and effect relationship with anything.