Yes, you can change your course later if someone drops Classics 1B03. Just keep checking SOLAR! It remains open to you for seven days from when you started your registration, so keep checking back every day, multiple times per day. I've heard a rumour that around 3:00am is a good time to grab course openings, haha. Once SOLAR closes, it will reopen later in July, and then you can start trying to get a spot again. And if all of that fails, you still have a week or so once classes start in September to add/drop courses.
Don't worry - although not guaranteed, you probably have a good chance of getting a seat in that course eventually. I hope that helps!