After the ownership documents exist and before the transferee is needed on site. The qualifying relationship must be real at filing, so a petition submitted before the share transfer closes has no group link to point to.
Fix the order of events
Set the order as: close the acquisition, record the new ownership in the share register and any regulatory filings, confirm the U.S. entity's trading status, then file. Hypothetical example: a Lévis industrial-coatings company signs a letter of intent to buy a U.S.
applicator in March, plans to close in June and wants its technical director running the site in July. Filing in April, on the strength of the letter of intent, invites a refusal because the affiliate relationship does not yet exist. Filing the week after closing, with the purchase agreement and updated share register attached, is the earliest defensible date.
From there, add current USCIS processing time, or premium processing where the company chooses to pay for it, and tell the U.S. site the realistic arrival month. If the transferee must visit earlier to inspect equipment, keep those visits within what a business visitor may do and keep them short, because those days do not count toward anything.