During the first year that my local sorority was in existence, they could not participate in formal recruitment, but they were allowed to have an information table where PNMs could stop by between parties, chat briefly with a sister or two, and pick up a rush schedule. Rush was held the following week. (A rho chi even stayed deaffiliated to distribute bids.)
The following year, Panhel invited my local to participate in FR. It was a disaster.

As a new, local sorority with only 12 members and no alums, we simply didn't have the resources to compete with four well-established national sororities with 70+ active sisters each and strong alum support. We took zero pledges.
Looking back, it would have been better if we had just participated in round 1, given a little presentation to the PNMs as to who we were, and then stepped back and held our rush after the conclusion of FR. You could propose that; if Panhel doesn't bite, try the information table idea.