The capital must be invested or actively in the process of being invested when the petition is filed, so waiting for approval is not an option. What can be sequenced is the family's move: they should not relocate on visitor entries while the petition is pending, and the contractor's management must be shown without unauthorised US work.
Invest at filing, move at approval
An EB-5 petition is decided on an investment already made or irrevocably committed, so the contractor's money has to be in the enterprise's account or in an escrow with release conditions before filing. Hypothetical example: a Lake Country contractor forms the Arizona enterprise, capitalises it with the full amount, signs the plant lease and orders equipment, then files; the plan shows hiring over the following two years. During the pending period he may visit Arizona on business to negotiate and supervise set-up, but he cannot work there without status, so day-to-day management before approval should be through a hired US manager acting under his written direction from Canada.
If the timeline demands that he be present sooner, a separate nonimmigrant category may be considered on its own merits. Once the petition is approved and a visa is available, the family completes immigrant visa processing and enters as conditional residents; the two-year clock to Form I-829 starts on that admission date.