What is your logical/probable take on how it all began, starting from nothing? And please include evidence to support the claims.
Science posits the big bang to explain how the universe expanded from an embryonic universe to the one we see today. How the universe came into existence is pre-big bang and lots of theories abound, none of which involve a deity.
One possibility is that 'nothing' is unstable. This instability caused a matter/anti-matter particle pair to spring into existence. This doesn't violate any physical law because the sum of these two particles is zero. Normally, these two particles instantaneously annihilate one another. All this has been reproduced at Fermilab and so is not a far-fetched idea. It actually has credibility.
Circumstances may have arisen where the matter/anti-matter particle pair did not annihilate one another and more particles came into being.
Where did the mass come from?
Nowhere because no mass was created because the particle pairs have zero mass.
We know from observation that certain matter particles can become anti-matter particles and vice versa. CERN has verified this. We also know that the conversion rates are asymmetrical and anti-matter particles are converted to matter particles faster than the reverse. This has also been verified by CERN. This creates more matter than anti-matter particles such that, when particle annihilation takes place, there is an excess of matter particles left over which become our universe.
Now, just because this is possible, it doesn't mean that it happened.
Notice that there is no need for any deity of any kind.
When the universe came into being, so did space-time.
Now, here's the thing. In our universe, an effect doesn't happen without a cause. Cause and effect are time dependent and cause always precedes effect.
Before the universe came into being, time did not exist. It is therefore entirely possible that there can be effects without a cause. In other words, there didn't need to be a cause or a causal agent for the creation of the universe. However, it has to be said that science has no idea what physical laws, if any, applied pre-universe. That said, because science doesn't know what caused the creation of the universe, it doesn't mean that god did it.