Anything that begins to exist has a cause.
This is not known to be true. We've never witnessed something "begin to exist" via a cause. Causation only applies to existing materials transitioning from one state into another state (nebulae into stars, trees into furniture, etc.)
And the only thing we've ever witnessed "beginning to exist" are virtual particle pairs - which don't have a cause as far as we know.
An expanding universe must of had a beginning.
Once again, this is not known to be true. And if space-time began with the universe than saying "the universe began to exist" and "the universe has always existed" are identical statements.