There is no fixed waiting period and no reliable general answer. The timing depends on how the qualifying period is counted in this history, how much evidence of the new authority exists, and the organization's needs. Counsel should assess the specific dates before anyone commits.
Set the review before the start date
Sequence it as assessment, then evidence gathering, then drafting, then the applicable case steps, and only then travel. If the business has promised a start date, tell counsel at the first meeting so the advice addresses it directly. Petition approval, visa issuance where applicable, admission and permission to work are separate, and the last of them controls when work can lawfully begin.
Add one dependency to that sequence: the availability of the people whose accounts the assessment relies on. A manager who can confirm what the earlier role involved, a finance lead who can produce approval records, a colleague who witnessed the handover — each has notice periods, holidays and the possibility of leaving, and each is a single point of failure that no schedule accounts for by default. Ask early whether anyone in that group is departing, and take their statement first if so.
Hypothetical example: a cybersecurity company's outgoing regional manager, the only person able to describe the pre-promotion role from direct knowledge, has three weeks left, and the schedule is reordered to take that account immediately rather than in its natural position after the corporate documents, which is the difference between a strong file and an explanation of why a strong file was not possible.