Close first, register the share transfer, then file. Filing before closing risks a denial on the qualifying relationship, and a denial is far more costly than the weeks saved. Where the buyer needs someone on the ground immediately, that need should be met by business visitor activity, not by working.
The closing date sets everything else
Work backwards from the day the transaction completes. On that day the ownership chain becomes provable, and the corporate documents the petition depends on come into existence in final form. Before it, the file rests on conditions that may yet fail.
The gap that creates is real, since a buyer usually wants its own person supervising from week one, and it is where mistakes happen. Attending meetings, negotiating, reviewing the operation and reporting back are ordinarily business visitor activities; taking charge of staff and running the production floor is not. If the newly acquired entity is a corporation formed for the purchase and has been operating for under a year, the new office rules apply and an initial approval of one year should be expected, with an extension turning on what the entity can then show about premises, staffing and activity.
Plan the first twelve months as evidence gathering.