The skip button has to be pressed before the timer runs out since the timer is supposed to be for the whole game not just for the build phase, that clearly was a confusing choice, and then there's a bug that the game doesnt end when the timer runs out and you were still in the build phase, so even more confusing.
But essentially if you'd like to try again, make sure you skip before the timer runs out, that way you'll be able to experience the other half!