I have a Canon M3 with Godox X1T-C and TT350-C. It seems the two Godox units are working with each other but my Canon M3 isn't. When I press the test button on the X1T, the TT350C flashes. It even flashes when I mount the trigger on camera. I checked online and the trigger is listed as compatible with my camera.
If the transmitter already works with the flash, then the usual stuff seems to be ok. The flash may accidentally fire when putting the transmitter on, as the pin for firing my be shorted when sliding it into the socket.
Note that the X1T-C transmitter needs firmware V22 to work with the M3. Current version is V27 from 2019-06-18.
Also the TT350C needs v1.5 for M3/M5/M6 compatibility.
Please make sure both devices are patched up to current firmware levels. Some more details on that: How do I tell if my Godox trigger or flash needs a firmware update?