This is actually an interesting question because if you seek an opinion about things that mainstream theories do not explain there is quite a list:

Does Big Bang Theory explain how expansion of our observable universe began?

No. It starts an instant after the “big bang”.

Does Big Bang Theory explain what caused the big bang?

No. It doesn’t even say there was a Bang as such. The term “Big Bang” came from an early detractor of the General Theory of Relativity as an effort to discredit GTR. Obviously the name stuck but the theory never mentions a starting point, a Big Bang, or what might have caused the expansion.

So some of the things my ATM theory tells us that mainstream theory does not are:

• What preceded our Big Bang universe.
• What caused the expansion of our early primordial universe.
• What was the primordial soup composed of.
• What causes matter to form.
• What happens to matter that forms within the expanding universe.
• Why can’t we detect the greater universe.
• Why does it seem like there is no center of expansion, i.e. how can it be that all galaxies are moving away from each other at the same rate.