You need to find out when the new job’s insurance starts, which is usually on the 1st day of the month (30 to 60 days). Then you need to find out when your current employers insurance ends. It could be on your last day of working, or on the last day of the month that you work.
If your current job has cobra, then buy the cobra (till) the new employer’s insurance starts and cancel the cobra.
The ACA now prohibits pre existing conditions.