Are there universities?
Yes. But you may need to game the system. A former friend and co-worker of mine was a high school dropout. After bumming around on a motorcycle and playing bass in a band for a few years he decided he wanted to be a doctor. Rather than compleing the GED, he enrolled in the evening college at University of Cincinnatiwhich, like many community colleges and branch campuses and night schools, was open-admission with no requirements. After he completed his first term with a 4.0 average, he took his grades to their College of Arts and Sciences and asked if they were good enough for him to transfer in. He knocked out his pre-medd BS in 3 years by attending 2 different universities, got into University of Kentucky med school, and now has had a long career as a general practitioner in Indiana. Still is not a high school graduate. So yes, it does happen.