Advancing Government Innovation with Leading-Edge Procurement Act of 2022 or the AGILE Procurement Act of 2022 This bill addresses federal procurement policy and barriers to entry in federal contracting. Specifically, the bill requires the Office of Federal Procurement Policy (OFPP) to pilot a program for entry of junior and mid-career professionals to the General Schedule Contracting series workforce, including by (1) considering the inclusion of program participants from other job series and fields, and (2) providing alternatives to education and training requirements for entry into the General Schedule Contracting series workforce. The Federal Acquisition Institute must (1) incorporate experiential learning into the training framework for the General Schedule Contracting series, and (2) provide a cross-functional information and communications technology acquisition training program to acquisition workforce members involved in acquiring information and communications technology. The OFPP shall issue guidance (1) to inform executive agencies on the availability of streamlined and alternative procurement methods for procurement of information and communications technology; and (2) on when a wider range of projects, as well as government projects, should be accepted as relevant past performance. The OFPP must (1) convene a working group or an appropriate existing body to make recommendations to reduce barriers to entry for entities seeking to do business with the federal government, and (2) expand a pilot program to use noncompetitive procedures for certain follow-on contracts to qualified businesses wholly owned through an Employee Stock Ownership Plan.