The time depends on whether the employer can promptly confirm the actual work and reconcile conflicting information. A cosmetic edit may be quick; resolving uncertainty about what the employee will do is a different task. Keep the proposed start date separate from assumptions about drafting turnaround.
Use factual sign-off as the milestone
Identify the supervisor and employment contact who must review the content, then agree on a response date with them. Once the facts are settled, assess the category and credentials before producing a final signed version. If new duties emerge during review, allow the eligibility analysis to change rather than insisting that the original category be preserved.
Do not begin U.S. work while a letter is being corrected; confirm the required authorization and its conditions first. Use a factual sign-off as the milestone rather than a version number.
The letter is finished when the person who understands the work has read the final text and confirmed that each statement is accurate, and when nothing in the company's other records contradicts it. Count backwards from there. Allow for the fact that letters typically require several passes between a recruiter, a manager and sometimes counsel, and that each pass depends on people whose priority is their own work.
Where a company has already produced two versions, expect diminishing willingness rather than increasing speed, and consolidate all outstanding queries into a single request instead of returning repeatedly. Avoid resigning or committing to a start date against a draft, since a document still being negotiated is not evidence of anything settled.