Far enough to complete the corporate documentation, confirm the qualifying year and prepare the evidence before filing, then add the responsible agency's current processing time for the route chosen.
Governance work sets the schedule more often than adjudication
Hypothetical example: the company decides in June that the president should be in place by September and treats the filing as the only step. In practice the longest stage is usually assembling what does not yet exist: a chart that reflects reality, a written record of delegated authority, minutes recording the board's actual level of involvement, and clean share registers for every entity. That work involves a corporate lawyer and the shareholders and cannot be rushed by an immigration deadline.
Once the file is ready, processing time depends on the agency's current published estimates, with premium processing available at extra cost. If the American subsidiary is under a year old, expect an initial one-year approval and an examination at extension. Set the operational plan around the later date and keep the Picture Butte coverage arrangements running.