That is difficult but doable. However, the bigger thing you'll be missing is the ability to work with programmers who are better than you. Freelancing is usually a lonely pursuit and you'll tend toward work that you can estimate accurately and execute efficiently. The need to focus on and master a domain is good for your consulting business but bad for learning. So I'd recommend against freelancing just out of university purely on that basis; you're missing out on the exposure and learning you'd get working in bigger teams.
That said, you don't automatically learn from people just by working in the same building as them, and you don't necessarily have to be a lone wolf when consulting. Whatever you choose, keep learning.
A freelancer is more of an implementer whilst a consultant helps to decide what is implemented.
Simple to get started, just find clients who need your knowledge and will pay you for it. Simple, but not easy...
Be warned that as a recent ex-student, many will see you as a cheaper alternative to more experienced professionals ("looking for student or recent graduate" in freelancer wanted ads is usually code for "I pay way below market rates").
It's not impossible, but it might be difficult to make livable money at first. I was freelance straight out of college and in hindsight a year or two at an agency or startup would have given me a big step up as I spent the first few years re-discovering things that an agency job would've taught me very quickly (specialize, pick a profitable niche, don't be afraid to fire clients/turn work down, etc).