Not before the project and its subscription terms are chosen, because the withdrawal triggers tax and leaves large cash idle. But the withdrawal must be complete, and the funds transferred, before the petition is filed.
Choose, withdraw, transfer, file
Hypothetical example: a Rothesay executive is told by a promoter to liquidate his RRSP now so he can move quickly when the right project appears. That advice creates a tax event and an idle balance for an uncertain purpose. The better order is to complete the source-of-funds documentation, select a regional-center project after reviewing its offering and designation evidence, agree the subscription terms and escrow, and then make the withdrawals in the tax year and manner the adviser recommends.
Once the net funds are transferred to the escrow under the subscription agreement, the petition can be filed. After filing, the stages are USCIS adjudication, visa availability, consular processing, admission as a conditional permanent resident, two years of residence and then Form I-829 filed within the ninety days before the conditional period ends. He should keep his New Brunswick home until the immigrant visa is issued and plan his time in Canada afterward with residence rules in mind.