Hi Blake,
Congrats on your education. I am also an accountant and know how tough those classes can be. I agree with the advice above. I have been out of school for 2 years now, own one SFR and have completed one fix n flip.
First, I would suggest using your accounting degree to find a job auditing or accounting for an investment company (real estate or not). This will help you develop an investors mindset and see the ins and outs of different strategies of raising capital, leveraging assets, etc.
Second, find ways to cut costs. Think along the lines of lengthening your student loan to the maximum payoff period and only make the minimum payment (stick with me here). If possible, move in with a family member to eliminate rent or at least minimize it. Don't go out and buy a fancy car like most college grads do.
Next, PAY YOURSELF FIRST. Set up a separate savings account and send a certain percentage of your paychecks directly to this account. This is the best way to build your capital for your first investment.
It may take some time to build a chunk of capital for your first investment so in the meantime, read as many books as possible (I suggest rich dad poor dad as your first), listen to the BP podcasts, and try to find a mentor who you can bounce ideas off of and possibly show you around your local markets. This will help you develop the base in which you will use to decide whether something is a good purchase in the future. Really listen to not only what has made investors successful, but also where and why they have lost money. It's much cheaper to learn from other people's costly mistakes than to make them on your own.
If you put in the hard work and research, your investments will by far exceed the benefit of paying off your student loans as fast as possible and I can guarantee you will be glad you got the w-2 job to subsidize your income until you can develop an investment base.
Good luck and stay eager!