“The closer we get to the Big Bang, the more ordered the Universe becomes. ”

I am not sure what this really means Darryl. Do you have an example, or picture how this “order” manifested itself?

“And random chance simply isn't a good explanation,...”

This is why I suggested to throw out the concept of “random chance”. It doesn’t really help comprehension. For example:

“even if you invoke a multiverse of alternate universes exploding randomly into other dimensions. ”

IMO, a situation composed of “a multiverse of alternate universes exploding randomly into other dimensions,” hardly seems a situation defined by order.

“The only realistic premise is that the Big Bang was a non-random event.”.

Knowledge would have us place what we know into a context of space and time, causes and effects, the non-random. But immediately some human mind is trying to work out around this order! “What if the Universe began a second earlier than it did,...or later?

I just think the random/not-random debate is unhelpful to say the least. But that will not stop anyone!