Argumentation

Statement: God does not exist

Reply: Show that this is the case.
Statement: But it's impossible to prove a negative so I could not possibly have a burden of proof!
Reply1: It is perfectly possible to prove a negative by showing a conflict in the definition or by highlighting something that would be expected to be true given the definition but isnt. Example: A square circle cannot exist because something cannot both be square and circular at the same time. The statement "there are no people in France" can be shown to be false by showing that there indeed are people in France.
Reply2: If it indeed was the case that it was impossible to prove a negative that still would not mean that you would escape a burden of proof with regards to the statement that God does not exist. It would simply mean that you are unable to provide such evidence and your position on the matter is irrational.