Your qualify event for COBRA is your last date of employment or last date of coverage depending on how your company’s agreement with the carrier is worded.
The company must give you COBRA information within 14 days of your qualifying event. You then have either 45 or 60 days to enroll under COBRA.
If you are picking up benefits after 30 days, wait with your COBRA election until then. If you have medical expenses within those 30 days that exceed the cost of the COBRA, enroll, if not , don’t sweat it.
By the way, if you had group medical coverage at your previous employer, the new employer’s medical plan can not refuse coverage due to pre-existing condition so long as the GAP in coverage is no longer than 63 calendar days. If you are picking up benefits after 30 days, the pre-existing condition is of no importance to you.
As always ask HR at the new job to confirm what I just wrote.
SRM