Tektronix and LeCroy and other make fine 'scopes.
I am sure that they make a device that can measure what you want.
set the scope to single trace and trigger on your start signal
tektronix TBS2000 series
https://www.tek.com/datasheet/digital-storage-oscilloscope
2 and 4 analog channel models
100 and 70 MHz bandwidth models
Up to 1 GS/s sampling rate
20 M record length on all channels
5 year warranty
I used a 4 channel LeCroy more that 25 years ago that could trigger on some event, and the recorded information
could be before the trigger or after the trigger, with the amount before or after could be adjusted