Firms hiring people with <1 year experience?

I'm currently a software engineer at a Fortune 500 company who recently just found out about the world of consulting, which I somehow never considered a career option. Are there firms that would hire consultants (management, strategy, technology) for college graduates with less than a year of unrelated experience? My long term career goal is to work for a few years, get an MBA, and work in either an operations or strategy role.

My stats aren't great. I majored in Computer Science at a really good public school for engineering (but not so much for business), and had a 3.21 GPA. My work experience is all in software engineering, and my extracurriculars have been pretty focused on entrepreneurship and founding startups (where I had a varied role consisting of business planning, management, customer discovery, as well as software development).

The reason I want to get into consulting now is because I did a case competition senior year of college (won 2nd place amongst mostly MBA students!), and learned through others about what consultants do and how it's a better career launcher than what I originally thought.

I was wondering whether it's worth my time for me right now to apply to consulting firms, because I'm not even sure I'll get considered for an interview. If so, I'll probably get help on my resume and start applying.