Goddard's first liquid fueled rocket in 1926 was pressure fed -- the engine was above the tanks, so gravity feed was not feasible. Liquid oxygen was vaporized with a small alcohol burner, and the resulting oxygen gas pressurized both the LOX and gasoline into the combustion chamber.
The V2 is claimed to have the first "large rocket engine" to use a turbopump, produced starting in 1942, but von Braun was working on turbopumps from 1935. The V-2's immediate predecessors, the 1936 A-3 rocket and 1938 A-5, were both pressure fed.
I don't think any "serious" rockets were ever flown with gravity-fed engines. Pressure-fed systems are fairly easy to manage (witness Goddard), and vastly increase the potential power of a rocket engine.
There are some problems with gravity fed engines:
- Chamber pressure must be low.
- Feeding pressure increases with acceleration.
- Rockets should be tall to increase pressure.
- Pressure decreases when tanks are discharged.
- Short experimental rockets are impossible.
- Gravity feeding may cause combustion instabilities.
All three predecessors of the A-4 (V-2), the A-1, A-2 and A-3 as well as the A-5 were pressure fed.