Neither extreme works well. Funds must be committed before the application, but an outright closing before approval leaves the investor owning a business he may not be able to run. Escrow conditioned on visa issuance is the usual bridge.
Use the escrow to time the commitment
E-2 requires that the investment already be irrevocably committed when the application is made, which sounds like it demands closing first. In practice the accepted approach is an escrow: the purchase price is deposited with a third party under instructions that release it to the seller on visa approval and return it to the buyer on refusal. That satisfies the at-risk requirement while protecting the Boischatel investor from owning a company he cannot enter the country to direct.
Hypothetical example: a contractor buying a snow-removal business wants to take over before the first snowfall; the sequence is diligence in spring, purchase agreement and escrow in early summer, source-of-funds and business plan assembled alongside, consular application as soon as the file is complete, and closing on approval. Consular appointment availability varies and should be checked early. E-2 is granted for a defined period and renewed only while the business keeps qualifying, so the plan should show it will.