How can scientists estimate when the big bang happened?

I guess they'd do it by looking at when the term "big bang" started showing up in papers. Or, maybe by looking at TV Guide.

(Hint: I don't think "theory" means what you think it means.)

I'll answer the question you were probably trying to ask also:

A variety of ways that are probably too complicated to explain in detail here, but involve looking at redshifts of distant galaxies and the cosmic microwave background.