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?
Trivially provable compared to that which is in principle unprovable.
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.
Firstly, prove that you do or don't have completely undetectable elephants in your house. You can't. Why? They cannot be detected. Therefore you cannot prove they are there. Or not.
It's not a strawman argument. I'm not claiming this is your idea, I'm adding new concepts.
The point being that it is possible to prove a negative.
Perhaps in some well defined cases, but not in all or even most cases.
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.
Quite true - definitions are everything in this case. Terms have to be explicit, including what is meant by "God". This varies so much it's practically idiosyncratic with every person defining "god" or "gods" in their own way, slightly different to the next person. If you define your terms to suit, you can prove god exists or doesn't exist.
In summary: God may or may not exist, for values of ominpotence between 0 and 1.