You want to have at least a year to do your project, and if you start as a sophomore then you can prepare yourself with courses and reading as well. If you are a more advanced Freshman, then starting even then would be okay. In all unusual cases we are pretty flexible except that we insist on evidence of intellectual content. That advisor might be less involved that usual, but will act as a quality control. Those students working on projects can share their experiences with the others.
Faculty tell what projects they have available.
You can take reading courses with faculty on more advanced material. This year, the course will be taught primarily by Gasarch, assisted by Dorr and Perlis. In addition we might have a 1-credit seminar for graduating honors students in which they can present their work to fellow students. You get to do a project and see if you like research. This might help you decide about going to grad school.