There is no fixed waiting period and no guaranteed processing time. Work backwards from what must be true at the time of the application: committed funds, a real enterprise, and evidence of the investor's direction. The signing sequence should follow counsel's review of the actual contracts, not a general rule.
Use milestones, and leave the departure plan flexible
Set dates for the ownership structure, the funds trail, the operating agreement and the final review, then discuss travel afterwards. A prelaunch enterprise can be presented with credible commitments, so first sales are not universally required. Keep the temporary nature of the stay in view, since E-2 involves an intention to depart when status ends.
Avoid resignations, closings or school commitments that assume an approval date. Hypothetical example: a clinical chemistry instrument service business has signed a lease and a service contract but is waiting on an equipment delivery that has already slipped twice. The signed lease and contract are commitments and belong in the file now; the delivery date is a forecast and should be labelled as one.
Ask the supplier for written confirmation of the current schedule rather than repeating the original date, and decide in advance what the plan is if the equipment arrives after the intended start. Agree that fallback with the supplier and the landlord now, while both still have an interest in accommodating it.