Yes, you absolutely can start your course in the audit track and then upgrade to the verified track later, so long as the upgrade deadline has not passed.
How do I know the upgrade deadline?
Please note that upgrading grants you access to graded assignments required for the certificate. The sooner you upgrade, the more time you will have to work towards earning the certificate.
In self-paced courses, the upgrade deadline is usually a short time before the course's final end date. In instructor-paced courses, the upgrade deadline may be much sooner.
Where do I find the upgrade deadline?
You can find the deadline on the right side of the course homepage under Important Dates listed as the Verification Upgrade Deadline.
If there's no upgrade deadline listed there, then the upgrade deadline has passed.
It is not possible to upgrade after the deadline or the course end. If the course's final end date is approaching or has already passed, it will be listed under Upcoming Dates as well.