(note - this refers to art directors in graphic design and illustration. As John says, it means different things in other sectors - particularly advertising where it's not nearly such a high level. This is also based on the UK - other countries might have different standards)
Is it possible to go from Art Director to Creative Director? Yes, it's probably the most common route.
Is it possible to start out as an Art Director from college? Not really, unless you set up your own agency and it's an exceptional, amazing success. This is very very rare!
A better question might be something like: What's the best career path / entry-level role for someone aiming to be a creative director? See also What’s the difference between an art director and a creative director?
Art director is not a job anyone would normally simply get out of college... It's pretty much the top of the design world food chain. Probably less than 4% of professional designers reach that level in their careers (to be fair, not all of them are aiming for it).
To go straight into that level by setting up your own agency, you'd need loads of rare talent plus exceptional organisational skills (or, a very good business partner), loads of luck and good connections, and the ability to survive 1+ year of 12-18 hour working days doing everything for almost no pay. It takes a long time to build up a (paying) client base and your competitors will have a huge head start. Even then it'd be a big stretch to call yourself an art director until you were directing a team of more than three designers.
In many countries, even just getting a Junior Designer job or paid design internship straight out of college isn't easy. Like most industries where people actually enjoy the work, design is often a difficult slog to get into.
Just my personal view, but if I met an art director with less than 3 years' industry experience, I'd be very suspicious. I'd suspect job title inflation or nepotism. If I met an art director with less than 5 years' industry experience, I'd expect them to be a really rare talent to have risen up that fast, (and/or, that they art direct a very small agency).
Definitely aim for it if you think you've got what it takes - but (like anything worthwhile) be prepared for it to take a lot of work to get there!