Maybe not a bug but rather a design decision, but in hotlap mode, crossing the start/finish line for the first time (starting the first hotlap) does not send an IS_LAP packet, which means we have no way of knowing when this lap starts. This can be an issue for many possible reasons: triggering a new telemetry dataset, starting custom timing or delta time, etc.
Following IS_SPX and IS_LAP packets are properly sent, starting with split 1.

It might be related to the not getting an InSim signal for the green light - IIRC that was to thwart people who would make an InSim launch control from it.

It's not ideal, but you can calculate the time the race/lap started when the first car hits S1 - take that first split time away from the current race time for the exact time of the green light.