No, one cannot prove a negative, however this is not relevant.

The burden of proof is always on the person making a claim. It is not up to everyone else to prove you wrong. It is impractical.

Literally, there are infinite possibilities that haven't been proven to be wrong yet. That does not mean you go ahead and accept all of them until they are disproven.

Half the problem is that many theistic claims aren't constructed in such a way that they are falsifiable, to begin with. That does not make them automatically credible. That makes them automatically non-credible.

Ultimately, not proving that something does not exist does not lend that claim any credibility in any way, shape, or form, nor does it makes the belief valid.

As a general rule of thumb, if an argument you are using equally justifies an opposing viewpoint, then it is not a great argument. For instance, if I were to ask a Christian, "Can you prove that Allah does not exist?", he/she would scoff at the argument. Asking a Muslim, "Can you prove that Jesus-God does not exist?", he/she would equally scoff at the argument. Both, however, use the argument as a justification for their own religions.

Now, determine the permutations of 7 major religions asking each other that question, and you'll find that none of them find the argument convincing from any of the other religions' positions.

That is because the process of accepting claims as true until they are falsified is an invalid and inaccurate approach to gathering knowledge.