Does your proto use a microcontroller? Then you can use one of the GPIO pins to measure the time from the switch to the beginning of the USB3 transmission. You don't need a $50,000 scope for 1/10ms timing measurement, any entry level scope ($400-$1000) will work (Rigol DS1054Z, Micsig TO1104, Siglent SDS1202X-E, Keysight DSOX1102A, etc).