B737-800 pilot reported an engine failure during a Functional Check Flight after a heavy maintenance inspection. The crew was able to restart the engine and returned to the departure airport and landed.

Narrative

Crew conducted a Non-Routine Flight Operations 2 (NRFO2) Functional Check Flight (FCF) required for completion of a Heavy Check maintenance on aircraft X.While completing the inflight restart profile procedures (with proper 'Windmill start' parameters and envelope); the number one engine did not start--there was no fuel flow indication. Crew attempted two other relights with no success (within the proper 'Windmill start' parameters and envelope).FCF profile procedures stopped; and crew coordinated a return to ZZZ. Crew further completed the QRH Engine Failure or Shutdown checklist; resulting in the decision for an Engine Inflight Start (3AA-3PX). After careful assessment; situational awareness; proper conditions and within the 'Crossbleed start' parameters and envelope; crew restarted the number one engine and completed Engine Inflight Start checklist.Crew advised ATC as a precaution due to engine reliability.Flight returned to ZZZ with no further incident.Cause: FACTOR--Maintenance removed/replaced the number one engine Hydro Mechanical Unit (HMU). RECOMMENDATION--During major maintenance cycles; recommend proper quality assurance practices for this type of component.