As design standards evolved over time, it's always a debate what was the first true Autobahn / motorway.
A555 was originally built as a 'kraftfahrstraße', not an Autobahn. Although it was a controlled-access highway with four lanes, it did not have a median barrier.
AVUS (A115) was a race track and not a conventional public road until after World War II.
A5 Darmstadt - Frankfurt was the first Reichsautobahn built by Hitler. However the Reichsautobahn did not have paved shoulders as a design feature.
The first Autobahn with full shoulders was probably not built until the 1950s.
Likewise, the Italian autostrada evolved over time, but the name stayed the same. The first Italian autostrade were roads reserved for motor vehicles and were tolled, but they weren't actual motorways, many if not all of them built before World War II were single carriageway roads with 2 or 3 lanes total. A90 around Rome is usually considered to be the first modern autostrada (divided highway with shoulders), opening in 1951, but this was a very short segment. A7 Tortona - Seravalle opened in 1958 as the first longer segment of four lane divided autostrada.
In the Netherlands, the first precursor to the modern autosnelweg opened in 1933 between The Hague and Rotterdam, but it did not have divided carriageways (similar to A555 in Germany). A12 east of The Hague was the first motorway in Europe to incorporate both divided carriageways and shoulders in 1937. However the shoulders were laid with bricks at that time (it was an economic stimulation of the brick industry at that time).