Hello! Hopefully you are fine!
I have viewed your Wordpress-powered course-selling website and reviewed the "White Card" training course as an example.
At the right side under the caption: "Available Dates", it is showing what you termed as "variant". And, you only want it to be hidden from eyes of visitors when its date has passed. But, if a variant is full, meaning that the students have booked all the available seats, it will keep on appearing with the subtitle: "Sold Out" until the date has passed. So, the requirement is clear to me and I am ready to start work.
Please fell free to ask anything you would like to ask regarding my expertise.
Regards