A lot of people think of "contract" as specifically a written document, but that's not what a "contract" is in law, the written document (if it exists) can be very powerful evidence that (1) there is a contract, and (2) what its terms are, but contracts exist without them.

While US employment is usually at will without a defined contract term, there are mutually enforceable obligations, including some definition of what the employee is obligated to do for the employer and that the employer is obligated to pay the employee at some specified rate assuming the employee's obligations are met. That's a contract. Exactly what the detailed terms are may be difficult to prove absent a single comprehensive written document, but it is a contract.