The investment must be committed before the consular application, so the usual sequence is to sign, place the funds beyond recall and close, or to close subject only to visa issuance, and then apply. Do not start managing crews or bidding work in the United States until the visa is issued and you are admitted in E-2 status.
Commit the money, then apply, then work
The order matters because the commitment element cannot be satisfied by an intention to buy. Two structures are common. In the first, the siblings close, pay the seller, take title to the company and then apply for their visas, accepting the risk that a refusal leaves them owning a business they cannot run in person.
In the second, the closing is made conditional only on visa issuance, with the funds held so that they are released automatically on that single condition; this satisfies the commitment element if the only contingency is the visa. A closing conditional on financing, due diligence or the seller's licence transfer is not yet a commitment. Once the visa is issued, admission at a port of entry gives E-2 status for up to two years at a time, and the visa itself may be valid for up to five years.
Trips before issuance to inspect the yard or meet the accountant are visitor activities; supervising a roof crew is not.