Rather,
No, you don't have to be on final at MDA. It would be impossible. If you had to maintain, say,a 900 ft MDA inside a 2NM circling area, and take into account a turn radius, you would be at 900ft at 1.5nm, around 500ft high and in no position to make a stable approach. Descent can start anywhere on the projected 3 degree flight path.
As to the FMC, easy, you don't!! A centre line and trend vector can help (provided you have a good FMC update), but this is a VISUAL proceedure. Break out the old Eyeball mk1.