That depends on the registrar's stated release date and on whether the other records already establish the credential. If they do, waiting may be unnecessary; if they do not, a start date built on an estimate is fragile. Ask for the release date in writing.
Let the registrar's written date drive the schedule
Verbal estimates from a front counter shift; a written date from the registrar gives the employer something to plan around. If the release falls after the intended start, discuss with counsel and the employer whether the filing or entry attempt should follow the transcript rather than precede it. Avoid committing to travel, housing or a resignation date until the record situation is clear.
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. Plan instead from the licensing board's written processing estimate and the certification body's timeline, whichever is longer, and add a margin for a request for further documents. Without the employer's written description the support letter cannot be finished, and an applicant who appears at the border with a vague letter risks refusal.
A foreign credential evaluation takes as long as the evaluator takes.