Stump the Christian?

[Randy Carson]

Also special pleading, asserting that god is not subject to infinite regress

See, there you go again conflating 'beginning to exist out of nothing' and 'beginning to exist by rearrangement of things that already exist'

A little more here since "conflating" is your problem, not mine.

The Contingency Argument states that “everything that exists has an explanation.” The explanation would be either in the necessity of its own nature or in an external cause.

Opponents of theism frequently confuse or conflate the Contingency Argument with the Kalam Cosmological Argument by arguing something such as:

1. Everything that exists has a cause.
2. If God exists, He must have a cause.
3. Therefore, God has a cause.
4. But anything that has a cause cannot be God.
5. Therefore, God does not exist.

This fails because Kalam states "begins to exist" - not merely "exists".

But then opponents of theism often claim that this is “special pleading”; however, atheists themselves often argue that the universe - matter, energy and time - have always existed. Therefore, it is not special pleading for the theist to argue that God has always existed.

Bottom line?

No Composition Fallacy.
No Fallacy of Equivocation
No Special Pleading.
No idiocy.