There is a HUGE amount of confusion about what at-will employment means. If we are all going to be advocates for cultural change around work in the US, we need to better understand it. I've been a labor and employment lawyer (for workers and unions exclusively) for nearly three decades. THIS IS NOT LEGAL ADVICE, it is instead a discussion of legal doctrine that is only somewhat uniform across the 50 states. Applying this legal doctrine to a particular set of circumstances requires the services of a lawyer who actually knows your state's laws.
A contract in US jursidprudence occurs when two parties agree to provide “mutual consideration” to each other as an exchange. “Mutual consideration” simply means both parties are getting SOMETHING out of the deal. If I promise “I'm gonna give you $10, just cuz” that is not a contract, becuase there is no mutual consideration. It becomes a contract only we agree “I'm gonna give you $10 to wash my car.” That's mutual consideration. If one side offers a deal with mutual consideration, the other side accepts that offer, you ahve a contract. That simple, nothign else required unless specific rules about the subject of the contract apply, and there are very few common law rules about contract requirements for employment.
The at-will doctrine says ONLY that if the contracdt does not state a specific term, or a specific limitaiton on gorunds or methods of contracdt termination, then either side may terminate the contract at any time for any reason. If I say “I will pay you $10/hour to clean my house once a week,” and you accept, we have a contract. The at-will doctrine states that contrat may be terminated at any time by either party, for any reason or no reason at all. It's still a contract, just a termianble one. If you spend 10 hours cleaning my house, I owe you $100. I can terminate the contract right then, and I still owe you that $100, but you can't come back after I terminate it and clean my house again and expect to get paid.
Everybody who is an employee has a contract. Let me emphasize that: EVERY EMPLOYEE IN THE US HAS A CONTRACT. It just may be a shitty contract that can be terminated at any time, but you still have a contract. That contracdt may not even be in writing, it doesn't have to be in writing. Contracts can be verbal, or their terms can be established purely through the actual practice of the parties. But everyone should stop claming that because of the at-will doctrine, there is no contract.