"Joe" wrote
The universe (including time itself) can be shown to have had a beginning.
.... Correct?

No! There have been and will be many universes cut from the same cloth.
Moreover, time is not necessarily linear. Only segments of time have a
beginning and an end.

It is unreasonable to believe something could begin to exist without a
cause. ... Correct?

No, wrong again. MOST things begin to exist randomly, with no cause in the
sense that you use the word here.

The universe therefore requires a cause. ... Correct?

No, because your thesis is wrong. Which universe are you talking about?

Einstein's theory of general relativity shows that time is linked to
matter and space. ....

Einstein's theory is a useful tool but does not and cannot describe the real
universe. It cannot because the mathmatics used cannot deal with infinity
and the universe, or rather universes, are infinite. I can demo that 2=1 in
our math so ....

God, as creator of time, is outside of time. ....

That might apply to the Taoist abstraction hardly to the "god" Jews,
Christians and Muslims believe Abraham encountered (Gen 18) hoofing across
the desert at high noon on his way to check out rumors.