I am currently learning complexity theory and wasn't able to find a tightest lower bound to BigOmega(n!), I am quite certain it isn't n^n and so wasn't able to reach to a tightest lower bound, can log(n)^n be the one, of course lose lower bounds are possible, but can you please help me understand the tightest lower bound of n!?
You are indeed correct that it isn't $n^n$ (though this is good enough for most purposes). As OmG mentioned in the comments, there is a standard approximation formula called "Stirling's approximation formula" which gives the following asymptotic bound: