Acceleration hesitation on cold start

2003 Ford E-150 4.6.
Runs okay for first thirty to sixty seconds. Stop vehicle at a stop sign or light, hesitation on slow acceleration. After that it runs fine, until the engine is turned off and let cool down for twenty to thirty minutes, the problem then reoccurs. If idling for four to five minutes, before pulling out of driveway, runs fine. Fourth mechanic. No discernible codes. Newer coils. New fuel filter, fuel pump, oxygen sensors, air filter, EGR pressure sensor, battery, alternator. What gives?