Start as soon as an offer looks serious, because registry copies and institutional letters are often the slowest items in the package. Waiting until an employer sets a start date leaves no room if a record has to be ordered from another jurisdiction.
Order the slow documents first
Civil registries and universities work on their own schedules, and requests made from abroad can add weeks. Place those orders while faster items, such as the employer letter and duty description, are still being drafted. Keep travel and resignation decisions flexible until the linking documents are in hand, since an incomplete chain is a reason to postpone rather than to attempt an entry and explain afterwards.
Two clocks run at once, and they are not synchronised. The employer's clock is set by a project or a payroll date; the registry's is set by its own queue and is indifferent to both. Hypothetical example: a statistician whose transcripts were issued under a former surname is offered a role modelling insurance claim reserves from the start of the next quarter, and the issuing university confirms that it releases replacement transcripts only twice a year.
The real choice is then between a later start and a confirmation letter the university can produce sooner. Ask about that alternative early enough that it remains an alternative rather than a rescue.