Joining a professor's research group that is full I am starting my graduate studies in CS this fall. I had 1 particular professor in mind whom I wanted to work with. Before joining, I had a few emails exchanged where prof. asked to setup an appointment once I join to discuss projects.

Last week after joining, prof. told me that advising won't be possible in the fall since his group is already full. My research interests align very strongly with his, so I really want to work with him.

What I am not sure of is whether the group is actually full or he is not interested in working with me anymore. Any advice on how should I approach him again to inquire politely about possible openings in the future will be really helpful.  I am also taking his course to gain more knowledge and expertise as well as to demonstrate my interest. Would this be a good segue to discuss advising opportunity in the future?
Yes, it is a good way to get to work under him. By taking the course, Prof. will get to know you. However, you should do well above average in his course to increase the chances of joining his research group. I'd suggest that around mid-point of semester you mention that you still want to join his group on Spring. There is no point on hurrying things up yet, specially because he already said that his group is full.