Yes, I believe that would be fine. There are no caveats stated about using the CISSP as the CCSP experience waiver.
Whether you have become an Associate of ISC2 post passing the CCSP, or are just using the 9-month period you get to submit your initial CCSP endorsement, the process is the same.
Go through the CCSP endorsement on the endorsement portal, if you have an active CISSP at that point it should be detected, and the sections of the form related to detailing experience and identifying an endorser will be removed.
Good luck with your goals!
The Associate of ISC2 designation can be earned by anyone who passes an exam for a certification requiring work experience.
After you pass your exam and receive official notice from ISC2 to begin the certification application process, select Associate of ISC2 if you do not yet have the required work experience. You will be prompted to pay your first Annual Maintenance Fee (AMF) of U.S. $50. You will then join our global community of cybersecurity professionals who are working every day to achieve our vision of a safe and secure cyber world.