"jam ne" means "no longer" (like "ne ... plu") instead of "already not". But then how would one express the negation of just "jam"? That is to say, how to say that one has not already done something.
For example, if one already did something...
I {have done}/{already did} it.
Mi jam faris ĝin.
But then what about...
I {have not already done}/{did not already do} it.
I can imagine something like "mi ne jam faris ĝin", but I do not know if it would mean something else, like "jam ne" does, or if it would be understood differently.