Neither in pure form. Sign and fund the escrow first, apply with the closing conditioned on approval, then close on issuance. Closing outright before the decision leaves him owning a business he cannot legally run; applying with nothing committed leaves him without an investment to show.
Sign, escrow, apply, close — in that order
The two failure modes are mirror images. A buyer who closes before applying has met the commitment requirement in the strongest way, but if the visa is refused he owns a U.S. contracting company he cannot direct in person, cannot easily sell quickly and may have to run through a manager he did not plan for.
A buyer who applies before committing anything is told the investment is not irrevocable and is refused. The sequence that avoids both is a signed purchase agreement, the price and working capital deposited in escrow, an E-2 application supported by the agreement, the escrow instructions and the source-of-funds trail, and a closing that occurs automatically on visa issuance. Build the seller's patience into the deal with a defined outside date and an agreed remedy if the visa is delayed.
Licensing should run in parallel, since a state licence transfer or a qualifying-individual arrangement can take as long as the visa. Time the family's move, the children's school registration and any lease after issuance rather than after signing.