Back in the dial-up days, we used to connect though auto attendants, programming pauses to get the timing right. For sites that were live answered, we’d have the receptionist transfer us to the system modem and program our modem for reverse transfer.
What worked even better was transferring to a CRA that timed out to the modem with a 5 second pause.
Okay, I know this doesn’t help the OP but it’s fun to reminisce.