Advice for Managing LinkedIn Company Page Connections and Outreach

Hey folks - new here, need some general advice with LinkedIn. Created a company page just recently, linked to my profile and realized I can't connect or search for folks as "the company page". Now the only way I can invite people to connect with the company page is thru my network (which tbh don't match the ICP). Is there a better way to do this? Should I create a separate LI account entirely, then create a company page and start reaching out?