Unless you Protoss and mind control the Zerg, and then are Zerg+Protoss.
If you could win as Protoss by building Dark Archons, raiding your Zerg opponent's base to capture a worker, building a bunch of Zerg production and tech buildings, and attacking with a combined army... you most likely outclass your opponent, and could have won much faster using a more conventional strategy.
So there was enough time. The big risk was that the map would max before you could fully develop the Zerg side.