Know if a turkey is done cooking
Go get a $15 probe thermometer. There is really no point in cooking turkey or any other roast without one.

The actual answer is- there is no good way without measuring the internal temperature.
Any time-based approach will be a guess at best.

The built in thermometer in some turkeys is a spring with some epoxy that melts a specific temperature. They are somewhat unreliable and either way they spring at 180F or so. This is well overdone for white meat but covers the turkey seller's liability.

Really- it's worth it to just get the thermometer and take the guess work out.