Advisor meeting late, worried about courses filling up

I am a incoming freshman and I did my online orientation May 29th. When I went to schedule my advisor meeting, everything was booked and the first spot I could get was June 23rd. I know my course registration is on hold before I meet with my counselor, but I'm worried that the classes I may need will fill up (such as Intro to Research). I have friends who already have their schedule made and all I have done is add classes to my cart.

I am planning on being a psych major and doubling or minoring in neuroscience. Will the courses I need for gen ed or my major fill up by the time I select? I also have some AP credit which I mentioned in my survey.