If a new employer offers a start date, then rescinds the offer three days after you accepted, do you have grounds for a lawsuit?

Absent a SIGNED contract, it is impossible to breach the contract. In LIMITED cases, if you took action based on the offer that you would not have taken otherwise, you MAY have a claim based on "promissory estoppel'. If you think that applies to your situation, contact an attorney.

Unfortunately, everyone is an at-will employee, which means the employer can terminate you, or you can quit, anytime for any reason. However, if you can prove damages, such as moving to another city based on the promise of a job, you would have a basic contractual cause of action against the employer for recovery of damages in civil court.

Nope, you were not officially hired

You signed nothing, you received nothing (paperwork), you are not officially hired until you actually sign all the documents the company needs (tax papers, payroll)

Only if you have a written signed contract and you can demonstrate that you were caused genuine financial harm, for example that you turned down another job offer during those three days.

Probably not. First, a verbal offer or even a written offer is not a contract until both parties have signed it. If that had not happened, then there is not contract, and no law was broken. If the prospective employee knowing hid important information about themselves and the employer discover this, that would be grounds for rescinding an offer even it there was a contract because the omitted information nullified the contract.

For what?
What specific financial damages do you have because they, folded the store because of too many lawsuits,, for example??

you must be a youngster............the answer is no