No. A commercial deadline does not supply immigration permission. The genuine professional arrangement and appropriate process must support the start.
Separate acceptance from authorized activity
Identify what is agreed and what remains unresolved. A signed acceptance cannot guarantee admission or permit materially different duties simply because the employer needs someone promptly.
Before travel or productive activity, obtain the final duty allocation, confirm the US or foreign employer, the U.S. entity for which the activity will be performed, and the temporary engagement, and match the work to one listed USMCA profession and its qualification rule. Meetings booked around an assumed start date create pressure to proceed on assumptions, and moving a calendar entry is far easier than undoing an activity already performed. The usual failure is a slow start followed by a rushed choice: weeks spent waiting for an employer to confirm something informally, then a single week in which documents, a filing decision and travel all have to happen at once. Where the employer needs cover in the interim, that is a staffing question to be solved separately rather than a reason to compress the immigration one, and saying so early usually produces a better conversation than discovering it after a second attempt.