Treat the employee's start as undated until the status permitting it exists. The company controls only its own steps: internal approval, the online application and fee, and document submission. Vetting, the EB-1 or EB-2 determination subject to visa availability, and any interview are outside its control, and the published description in weeks is not a commitment.
Keep the role covered in the meantime
Do not build a project plan, a client commitment, or a reporting line around the employee arriving on a chosen date. Keep the current role staffed, and agree with the employee what happens to their existing position while the case runs. Have the finance team ready to move the gift promptly when instructed, since a delay at that point is one of the few timing risks the company can actually cause itself.
Add one further discipline to that plan: decide in advance what the company will not do while the process runs. An appointment announced internally, a team rebuilt around someone's expected arrival, or a named individual promised to a client as the lead on their account: each is a commitment that comes apart if the timing moves, and each tends to be made offhand by colleagues with no visibility of the case at all. Agree who may say what, and to whom, and keep the current role staffed until the employee can lawfully begin the new one.
Hypothetical example: a board resolves that nothing naming the employee goes to a client until a defined stage has been reached — a rule that costs the business nothing and closes off the likeliest route by which a schedule outside its control becomes a reputational problem.