Logic and reason only ever work on some set of underlying assumptions. In math, these are usually the assumptions of set theory. In the sciences, we have the assumptions related to testability vs knowledge.
But, any logical system that is strong enough to talk about the counting numbers (and has some other simple conditions) will have statements that can be neither proved nor disproved.
When it comes to resolving those questions, logic and reason alone cannot help. In a sense, then, there must be a 'leap of faith' whenever the original axiom system is extended. Logic can then take over, with the additional assumptions, to derive new results.
It may well be that religious questions are simply independent of other questions about existence, especially those leading to science. If that is the case, there is freedom *logically* to either assume or deny such questions. It is no longer a logical matter. it is then a question of which of various assumptions meet the needs for the ones making the assumptions.