As stated by @Corbett, having your GED should qualify you to apply for admission to a 4 year university, but you would also need to meet the university requirements which can be different from HS requirements.
For example, the UC’s and CSU’s have a-g course requirements that must be fulfilled to apply.
Going to a CC to strengthen your chances is a excellent route to take. The UC’s offer TAG (Transfer Admission Guarantee) if you meet all requirements and the Cal States have the AA/AS-T agreements that give transfers priority.
http://admission.universityofcalifornia.edu/transfer/guarantee/
http://www.calstate.edu/transfer/degrees/AAAS-TDegreeRequirements.shtml