Science is actually about How, Why, When, and Where. Time, Distance, Reason, etc. All of those things factor in. You can't build a model with science of how things work without also knowing why, when, and where.
Yet that does not disprove God, Jesus, etc.
It also does not prove them. That does not mean it WILL NOT.
You can certainly engage in what you called "thought experiments" and reach the HYPOTHESIS stage... after that it is purely speculation, and "what ifs". It is not proof of anything.
If you have data, and an experiment that improves it you document it thoroughly so other people can do the same experiment. If someone challenges a part of it, you do your best to answer that challenge with more experiments to debunk their challenge if possible.
I do truly view science and religion both as trying to answer the same questions. Personally I feel like religion takes a short cut because it only requires people to believe and have faith. In fact questioning that faith is usually strongly discouraged. That is one of the large areas that the two approaches diverge. Science doesn't care about faith, it cares about belief up to the hypothesis stage as that is basically what the hypothesis is, and then it goes on to try and experiment to prove that belief.