Don’t despair–it is often the case that seating fluctuates even after the semester begins. But here are some steps you can take now:
You should register for another class that you want to take (this is your Plan B).
Keep your eye on the seating availability so that if a seat becomes available you can add into that class, and drop the Plan B class.
Finally, if the semester begins and you still have not been able to add the class you really want to take, attend that class and speak to the instructor. It’s possible, though not guaranteed, that you’ll be added into the class.
And, if all of the above fails, take your Plan B class and wait for another opportunity to take the Plan A class!