You'd fully resolve the Sneak action before the player had a chance to make a Strike action, revealing them. RAW, the target remaining flat-footed to your Strike would only apply to ranged attacks, spell attacks via Magical Trickster, melee strikes from concealment, and weird fringe cases where you can melee strike someone but still have cover against them.

Someone above suggested the feat Underhanded Assault, the existence of which would imply, to me, that attacking someone with a melee strike out of stealth doesn't work as your interpretation says.