You have to wait for the host to finish.
Or, more precisely, you have to wait for the guy backstage who pushes his own button after the host has finished. If you push your button before he pushes his, you're locked out for something like half a second. His button is also connected to some light bulbs which are never shown on camera, which tell the contestants what's going on.
(But there are some human contestants who ignore the lights and try to time it anyway --- having practiced a lot at home, where they couldn't see them. One of them was a recent college champion, who was one of the pre-show speakers at a group viewing I was at for Monday's show.)