No reliable estimate is possible until the record is complete and reviewed, because some consequences are measured from specific dates. Treat any start date as provisional, and keep resignation, lease commitments and travel reversible until counsel has given an assessment.
Protect what is still reversible
The costly mistakes here are the irreversible ones made on optimism: notice given, a home sold, children withdrawn from school. Keep each of those open while the review runs. Tell the employer only that timing depends on a pending legal assessment, agree a point at which you will both revisit the plan, and set the next step by what the records show rather than by the calendar.
Because the route that applies depends on citizenship and current circumstances, and because each route has its own steps, a single promised date is not something counsel can responsibly supply. The window between a resignation and a last day is the most productive time to gather duty evidence, because the person who knows the role is still reachable and usually willing to help.
Identify the request date, available alternatives and the particular fact still unresolved. Agencies frequently work to a client start date and press for quick signatures.