Yeah, time travel probably isn't possible, but if it is, limiting the time traveler to only being able to go back to when the machine was invented at least solves the "why haven't we met a time traveler" problem.
It could also solve the "where will the extra atoms to instantiate a second copy of yourself come from?" problem if the machine uses some kind of filament to 3d-print the traveller.
sounds akin to how the transporter works in Star Trek