Only the first power plant in a black-start (like a hydroelectric dam or gas plant started by a backup generator) is truly "black started." The rest don't fit that definition because they depend on an external power source to spin up and synchronize frequency before burning fuel and supplying any energy to the grid. If they didn't, the second they'd turn on they'd experience catastrophic unscheduled disassembly of the (very big) turbines.
Only the first power plant can come online without the external transmission network.
In fact, if you’re not sure which will start first, you might go that way. They’re all disconnected from the grid at that time anyway.