I would love to engage both of you and several other professional mathematicians on the forum in a wide ranging discussion of complexity and evolution. But there are several different kinds of complexity involved, ditto for information, randomness and entropy - so to get the conversation started, we'll need to first agree to some definitions and meanings. On another thread, I've offered some general categories, if y'all would care to engage the debate. But, truly, I believe any discussion of origins or abiogenesis will quickly stall without taking that first step.
We have a similar need to arrive at some common understandings in the discussion of time and timelessness. As betty boop so beautifully pointed out, we who inhabit dimensionality (including one or more temporal dimensions) have great difficultly in apprehending the meaning of timelessness. That is true also of any "thing" which is non-spatial and non-corporeal.
The fact that our vision and minds are limited to four dimensions (three spatial and one temporal) although we can deduce that other dimensions likely exist - IMHO - is a good indication that there is a "beyond".
I believe StJacques is agreeing that the fact of a beginning (space/time) is also a very strong pointer. To that I would add the unreasonable effectiveness of math.
Hopefully, should we engage in the "complexity" debate, more people will agree that information (successful communication, not message) in biological systems is yet another such pointer.
At any rate, whereas such ponderings do not rise to the level of revealed Truth (Jesus Christ, the Word of God) - just doing the meditation can be important to Lurkers as well:
Excellent point, A-G!