My kid is a huge fan of flightradar so we spend way too much time watching it. I don't know the exact timing, but it is a consistent behavior that planes pop onto flightradar only a little bit before pulling out of the gate. But I'm not sure if there's a standardized point in the sequence when they turn it on or it's up to each pilot.

But you're right, watching the incoming plane to that gate would be a good way to know earlier!