I am about to finish my undergraduate degree at age 20 and I still feel like a little kid myself and I know I am not ready to start working, I still feel like I have a long way to go in order to become an adult. You may feel like that for a long time but you will be so busy with your studies that that won't even cross your mind, your undergrad degree will go by flying because you will be so busy so don't worry about having those feelings, in little to no time you won't even remember that. They will return once you graduate tho.