It is easily possible to prove something that does not exist.
I have no elephants in my house. Or I am not drinking alcohol.
Only true in the trivial cases where something is provable, but not true for all cases. Do you have invisible microscopic elephants that run from you when you attempt to investigate them? Have you drunk alcohol that tastes and smells like like water and does not get you drunk and that someone has been putting in your water pipes?
This is an illustration of why the burden of proof regarding the existence of god is with those who claim a god or gods to exist.
Since when are provable arguments trivial?
When the definition of elephant includes "invisible microscopic elephants" and the definition of alcohol includes "alcohol that tastes and smells like like water and does not get you drunk" then you may have a point.
But currently neither are true so your argument fails as a strawman.
The point being that it is possible to prove a negative.
This does not mean that it is possible that God does or does not exist, unless you define God as such that such a statement actually becomes provable.
Given that there is no universally consistent set of properties attributable to God that does make it harder to prove anything.