Both effective immigration work authorization and the conditions applicable to the actual laboratory duties must be satisfied. Ask which outstanding items prevent the proposed work from starting. A roster entry or a hiring approval does not itself answer those questions.
Coordinate dependencies without promising turnaround
Start necessary institutional requests once the applicable process is identified. Record which body controls each response and ask the employer to keep the start provisional. If the proposed first duties change to accommodate a delay, have those duties assessed before performing them.
Allow time for the credential review and the employer letter, then decide whether a same-day port-of-entry application or a petition with a written decision suits the risk. The corrected offer letter usually depends on someone at the employer who is not thinking about immigration. Renewal can be done by presenting an updated employer letter at a port of entry or by an employer petition before the current period expires. A Canadian citizen may generally seek TN admission at a port of entry, or the employer may file Form I-129 where suitable, but neither path is completed merely because funds arrived. A port-of-entry application can be decided the same day, but assembling a licence confirmation, translations and a correct letter typically takes several weeks, and an I-129 petition adds USCIS processing time.