In most states if you enroll in a private health insurance plan any time between November 1st and December 15th and make your first premium payment by the due date specified by your plan, your new health coverage starts January 1st.
After that, if you have a Qualifying Life Event and enroll between the 1st and 15th day of the month and pay your premium by the due date, your coverage begins the first day of the next month. So if you enroll on January 10, 2021, your coverage begins February 1, 2021.
If you enroll between the 16th and the last day of the month and pay your premium by the due date, your effective date of coverage will be the first day of the second following month. So if you enroll on January 16, 2021, your coverage starts on March 1, 2021.