According to my napkin math it would take longer than an hour if the tape was ~3.3*10^218 sec long (or three million trillion trillion… (18 trillions) …trillion years). Assuming you have only have two options to choose between but can pick which alternative in in 5 seconds (2^720) and you want to get down to a 1 minute intervall.
So i mean its not impossible to find a tape long enough though it seems unlikely that we would be so off in our estimates of the age of the universe.