Is it logically possible that Jesus was the son of god?
Was it logically possible that the Big Bang was a miracle of some bored gods?
What does it mean for something to be logically possible? What are the objective criteria to determine such a thing?
How does logic make things possible?
Does logic or modeling off data, or actual data, show it is possible or impossible to move faster than the speed of light?
There is no logic in saying because there was a yesterday that means there may have been infinite yesterdays. No logic to saying because the past is a mental collection of present moments those present moments were possibly infinite.
How does some idea with no evidence to support it become logically possible?
Logic doesn't make things possible; illogic makes things impossible. For something to be logically possible there are two requirements. It must not involve a contradiction in terms, and the criteria for it must be clear.
So, that said, no, it isn't logically possible that Jesus was the son of god or that the Big Bang was a miracle of some bored gods, because the words "god" and "miracle" have no clear meaning. It's of course logically possible to move faster than the speed of light; data and data models only address whether it's physically possible, which is a different question.
So what that means for an infinite past, anyone can figure out for himself. Is there anything unclear about what is meant by the hypothesis, "For every event, there existed at least one earlier event."? Can you exhibit a proof that taking that statement as a premise implies a self-contradiction?