Closing can proceed on that schedule; the visa cannot be assumed to. Structure the transaction so the business is properly managed in the gap between closing and issuance.
Plan for the gap between closing and the visa
Commercial timelines and consular timelines are independent, and the second is not controlled by the parties. A buyer who closes quickly must decide who runs the company in the interval: often the seller stays on under a short transition services agreement, or an existing supervisor is promoted with clear authority, and the buyer visits as a business visitor to attend meetings and review accounts without performing productive work. That interval also produces useful evidence, since a company that has been operating under the buyer's ownership shows commitment better than a plan does. What does not work is the buyer quietly running crews from Pennsylvania while the application is pending. Build the transition into the purchase agreement rather than improvising it after closing, and give the application the time the evidence requires.
Hypothetical example: a water-treatment-equipment distributor closes on a warehouse before the consular appointment is scheduled. The first review should decide who will lawfully receive deliveries, supervise employees and sign customer commitments until the investor has the appropriate status. The closing documents and transition-services agreement settle the interim authority. Arrange a manager or seller transition in writing before closing; the investor may visit for permissible business purposes but cannot use the pending application as permission to operate the warehouse day to day.