Do not resign from a Québec position until the credential the profession requires is issued and the admission route is confirmed. The immigration step is usually the shortest part; licensing and employer paperwork set the real timeline.
Put the slowest item first
Hypothetical example: a Lac-Beauport respiratory therapist assumes TN will take a few weeks because a colleague was admitted at the border in an afternoon. The colleague was a registered nurse with a licence already issued; respiratory therapy is not a listed profession at all, so the timeline question never arises until the category question is settled. For a listed profession, the ordinary sequence is: confirm the entry and credential, apply for any state licence, obtain the employer's support letter in final form, then decide whether to apply at a port of entry or by petition.
Give notice to the Québec employer only after the last of those is complete, or after a USCIS approval notice arrives if the petition route is used. Build the start date backwards from the licence issue date, not forwards from the offer. If the employer cannot hold the position that long, that is a fact about the job, and it belongs in the decision rather than in the file.