From the studies of the factory pilots' A-320 airshow accident (no advance to TOGA detent)
They were not factory pilots, they were Air France pilots. They would have got TOGA even with trust levers firmly stuck at idle if they only made that flypast 75 feet higher. You see, alpha floor is disabled below 100ft RA.
On the sim I´ve flown (if i´m free to use the expression) if you fly managed, your target becomes 250kt (adjustable through FMS) or green dot (if you fly selected). If you don´t like what your ATHR is doing - disconnect it as you pull it from TOGA to CLB. Ah yes, there´s airboos peciuliarity - ATHR is armed every time you make go-around so you have to press zee red bootons if you want to fly manually. Must be tough if you came from Böing.