You could try changing the engine oil and filter , using a good brand of parts . Some of the good filters have better anti drain back valves than the cheaper ones . This prevents the oil draining out the filter when engine switched off and helps on starting .
Have to be a very stupid mechanic that would start without oil in it . You should have returned the car immediately if this just started after replacing the sump . Changing oil filter also , not just engine oil is important . With the news about the sump been replaced puts a different slant on things as you have the oil pump , pick up tube and filter / screen now coming into play .