From OFCCP's perspective, there must be a way to satisfy the mandatory listing requirement. Any position lasting more than three days must be posted with the ESDS. If the staffing agency is posting their positions with the ESDS (and providing you with the applicant data for your annual adverse impact analysis on hires), and hiring the temporary employee on your behalf, then the subsequent move to a permanent position is an internal promotion. Otherwise, it will be up to the federal contractor to satisfy the mandatory listing requirement.
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.