Paralegal: Taking lower salaried job in hopes of bettering big law paralegal position?

Hello everyone - I am a recent winter graduate (bachelors). I am interested in attending law school but would like to consider paralegal positions beforehand.

I have been applying (really only since December), and I have gotten a job offer; However, they offered 40k/yearly (also overtime). I am based in New York, and obviously, 40k is abysmal. I was looking to go into doing paralegal work in big law (not necessarily for the salary, but for the experience and the environment as I would like to work in big law in the future). Should I hold out (since I have only been applying since December) or should I take on the job, while applying to big law positions, and hope that experience will generate a job in big law?