Start as soon as the offer is real. The application itself can be decided the same day at a port of entry, but the documents behind it, particularly credential evaluations and any state licence, run on their own schedules and are what actually determine the earliest sensible travel date.
The fast part is the decision; the slow parts are the inputs
It is tempting to plan backwards from the border appointment because that step is quick, and that is precisely the error. A foreign credential evaluation takes as long as the evaluator takes. A state licence, where the work requires one, is issued on the state board's timetable and cannot be accelerated by an employer's start date. An employer-filed petition on Form I-129 sits in a USCIS queue unless premium processing is used. Build the timeline from whichever of those is longest, then add margin for a document that comes back wrong, which happens often enough to plan for. And do not resign a Quebec position on the strength of a start date; resign on the strength of an admission or an approval, because everything before that is a plan rather than a permission.
Hypothetical example: a cartographer has a grant-funded start date but the final transcript has not issued. The review should decide whether the evidence can be complete before work begins, using the transcript, evaluation if needed, support letter, and licensing response. Work backward from the controlling evidence, then allow time for correction, adjudication, and any admission or consular step. Keep a written chronology of commitments and permissions. The planning failure is that a project deadline cannot create permission before the record is ready. Do not let a commercial schedule outrun the immigration record.