So, match the broadcast channel of the switch: toggle to the broadcast channel of the doors (assuming you're using a dynamic door object, like the Garage Door). You then just need to get them out of sync. I haven't done this before so here's what I'd try:

Have one door place at start: false, spawn time: 10 seconds.
Have a timer: on once with the same broadcast channel.

In theory, the timer should trigger one door to open before the second door spawns. At that point, one door should be open and one door should be closed. Now pressing the switch should close the open one and open the closed one.

This is all theory, I haven't tested this scenario you're describing, but based on my brief experience, this is what I would try.