It's possible to add Producer credits to your releases whenever you want, even if your release is already live in stores. Simply edit your release to include them.
To add a producer, simply go to the album page of the release you want to edit and click on the pen icon located at the top right corner.
Then, navigate to the "Songwriters" section on the edit page and click on the green "+" button. From there, select the "Producer" option and you're good to go!
Once you have chosen the "Producer" songwriter type, you may proceed to input the name of your chosen producer.