No, if you decide not to take COBRA coverage, you can enroll in a Marketplace plan instead. Losing job-based coverage qualifies you for a Special Enrollment Period. This means you have 60 days to enroll in a health plan, even if it’s outside the annual Open Enrollment Period.
However, if you enroll in COBRA you are likely not eligible to enroll in an individual health plan until open enrollment unless you have a qualifying life event (ie. getting married, having a baby) that makes you eligible for a Special Enrollment Period.