Unfortunately, there is no expedited processing for the I-526 approval or obtaining permanent residency. I-526 approval may take up to 12 months or more, and U.S. consulate processing of the permanent residency may take several months as well. If you can obtain a valid nonimmigrant status first (like an E-2) you can then apply through the EB-5 process and remain in the U.S.
The filing of the EB-5 I-526 investors petition does not authorize the investor or family members to stay in the U.S., during the adjudication process. The investor concurrently with the filing of the I-526 petition can also file other non-immigrant petitions to authorize the investor and family members to either live and work in the U.S., and even attend school. These non-immigrant statuses should have dual intent which allows the investor to still have the permanent intent to live and work in the U.S. and hence the investor can also file the I-526 petition.