An attorney would need to examine the agreement to answer your question.
What does the agreement say about termination? Employment agreements often specify that employment is "at will", i.e., that either party can terminate at any time, for any (non-discriminatory) reason or for no reason.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.
You should consult with an employment law attorney in New Jersey. The document you signed may or may not be a binding agreement; it is impossible to tell without reviewing it. If it is a binding agreement, you can break it but you may be subject to damages or the employer could seek an injunction to prohibit you from working with similar companies for a period of time. If it is not an employment contract, you are likely an "at-will" employee and so could leave your position at any time, with or without notice, in which case it would not matter that the start date has not arrived as yet. However, the attorney would also want to take a look at any other papers you signed in connection with this job. Often, at-will employees are required to sign non-compete and confidentiality agreements as part of the new hire process. If you did sign documents of this nature, the attorney can advise you of your rights even though you have not started work as yet.