I sometimes hear some pundit opining "You cannot prove a negative". Well, quite often, you can.
A simple example of proving a negative, is the proof that there is no largest prime number. And it's a very simple proof.
Here's an even simpler proof; in this case, I'll prove that there is no adult elephant in my office. Proof: if there were an adult elephant in my office, I'd see it, smell it, hear it and have difficulty getting in and out. But I don't see, smell or hear an elephant, therefore there is no elephant in my office.
The same principle can be applied to the proof of a great many negatives. In general, it takes the form of:
If X were true, then we would observe A, B and C. But we observe none of A, B or C, therefore X is false.
You can apply this to most claims of the existence of supernatural beings, especially gods.