Nope, students don’t generally have high enough credit ratings or enough assets to back thousands and thousands of dollars in loans. If you have to borrow to pay, the school isn’t really affordable.
How much can you pay without borrowing? If your child works summers they can raise ~$3k. With the ~$5500/year federal student loan that gives you ~$8k to start. Are there schools where your child will qualify for merit aid? If not, they may have to start at a community college. Most kids don’t attend residential college, so they’d be in good company.