Accepting a conditional offer and starting work are different acts. Make the start date contingent on valid work authorization and appropriate evidence. A spouse in qualifying E status is generally authorized to work incident to that status with the appropriate documents; another independent authorization may also be relevant.
Line up the employer's start date with the evidence
If the investor's funding still depends on a buyer's installment, explain that uncertainty to the prospective employer without promising an arrival date. Verify the spouse's lawful basis to work and required evidence, including an E-2S I-94 where applicable. Approval of the principal's case alone is insufficient.
Unmarried children under 21 may qualify as dependents, but that status does not authorize them to work. Hypothetical example: a spouse is offered a position with an environmental site assessment firm conditional on being able to start within two months. Answer that employer with the sequence rather than a date: what has to be approved, in what order, and what evidence would exist at the point work could begin.
Confirm the spouse's own basis to work and the document that evidences it, and keep that separate from the principal's case, which by itself authorizes nobody. If the household budget assumes the spouse's salary from a particular month, test the plan against a later start, because a funding delay on the investor's side moves everything behind it. Children in dependent status are not authorized to work by that status, so a teenager's summer job is a question to ask before it is arranged rather than afterwards.