If the Godox is Off Camera, it will be the Slave - the Camera is the Master.
Try settign the flash to slave, and see if that works.
However, just looked at the online manual for the TT350s, and it's not clear if it accepts the Sony wireless flash protocols
It does accept 'dumb' optical slave mode (where the Camera pop up Flash is used normally, and the off-camera flash fires in manual mode as S1/S2), but all the TTL descriptions refer to using one Godox as master, and another as Slave.
You can also use the XT1S trigger on camera.
The TT685S manual does refer to using the Sony optical wireless system - it might be worth having a look at that and seeing if its a problem with the documentation (IE if the way to set Sony Optical triggering for the TT685s will work for the TT350s).