There is a general answer about minors and contracts to the effect that minors can disaffirm the obligations of a contract. California law is a bit different. FAM 6750 identifies kinds of relevant employment, and the most relevant clause is (a)(1):
A contract pursuant to which a minor is employed or agrees to render
artistic or creative services, either directly or through a third
party, including, but not limited to, a personal services corporation
(loan-out company), or through a casting agency. “Artistic or creative
services” includes, but is not limited to, services as an actor,
actress, dancer, musician, comedian, singer, stunt-person, voice-over
artist, or other performer or entertainer, or as a songwriter, musical
producer or arranger, writer, director, producer, production
executive, choreographer, composer, conductor, or designer.
Such a contract required court approval. The question is whether the employment is for "creative services". Many programmers consider their work to be creative. In this case, though, the examples suggest that programming services are not included (invoking the interpretive canon "noscitur a sociis"). If the contract were covered by this condition, then FAM §6751 says
A contract, otherwise valid, of a type described in Section 6750,
entered into during minority, cannot be disaffirmed on that ground
either during the minority of the person entering into the contract,
or at any time thereafter, if the contract has been approved by the
superior court in any county in which the minor resides or is employed
or in which any party to the contract has its principal office in this
state for the transaction of business.
It is not illegal for a minor to sign such a contract, nor is there any law against a person making such an offer (although the employer has to have a permit (EC 49160; LC 1299). The minor can (somewhat) escape requirements of the contract, so it depends on what is required. In describing this as "at-will", I assume that there is no obligation to maintain the relationship for a particular period, meaning the minor can quit at any time and can be fired at any time. The contract presumably says "we provide X, you will do Y". Then the question is whether the employer can provide X, the minor can receive and accept X. but then opts to not provide Y while keeping X. An employer would normally sue for breach of contract, seeking the return of X. The minor could raise the defense "there is no contract", but that is an all or nothing proposition – you can't just repudiate one sliver of a contract. They can be required by the court to return any benefit received under the non-contract, although if that benefit is destroyed (spent, for instance), the employer would be out of luck. So the minor could be required to return X to the company.
An adult could "co-sign" a contract whereby they promise to pay a child's credit card debt, but an adult cannot bind a child to the terms of an employment agreement.