The assertion that He was God cannot be "examined on a consistent or rational basis." Thankfully, it does not need to be. Science will never prove God's existence, and Faith doesn't need to.
the person that did present Himself as God did show up, and he said no physical evidence whatsoever would be given. That includes evidence of design.
Or self-enforcing logic post hoc, ergo propter hoc. The point is, trying to use science to prove or disprove God is like using a can opener to catch fish: it's the wrong tool and succeeds only by chance.
Let the atheists believe (un-believe?) whatever they want. It shouldn't make one ounce of difference to a person of Faith.
If one has rational capacity, it must be. Judgement is required. That judgement is what determines salvation. That rational examination and judgement is what occers in John 6:44
"No one can come to me unless the Father who sent me draws him, and I will raise him up at the last day."
The draw is the judgement, that what God said about Himself is of beauty, value, worthy of praise and incorporation into one's own spirit.
"Thankfully, it does not need to be."
For those incapable of rational thought for whatever reason, that is true. For those capable of rational thought, it is not true, because they will make decisions and judgemnets in their lives.