Does the film actually show the submarine submerged for its journey?
Raiders of the Lost Ark is set in 1936, the pre-World-War-II era. Unlike nuclear submarines today, U-boats of that time weren't capable of long journeys while submerged.
U-boats traveled on the surface, propelled by diesel engines. They would dive to periscope depth to follow ships and attack. They would dive deeper only in order to avoid detection or attack by enemy ships. Speed was severely limited while submerged.
Because diesel engines need oxygen for combustion, underwater operation required electric engines powered by batteries. These batteries had to be recharged periodically by running the diesel engines—which, therefore, the U-boat could only do while surfaced. It simply wasn't practical or even possible for a U-boat to be submerged all the time;
Here are a couple of sources on this:
Unlike nuclear submarines, which could dive to depths of over 1,000 feet, travel thousands of miles submerged and remain on patrol for months at a time, the u-boat can operate submerged only for brief periods at a time. (source)
Because speed and range were severely limited underwater while running on battery power, U-boats were required to spend most of their time surfaced running on diesel engines, diving only when attacked or for rare daytime torpedo strikes. (source)
There was no reason for the submarine to submerge at all, even to periscope depth. Indy simply rode on the conning tower until the submarine got near the cave, and then jumped or climbed off.
(By the way, for a real-life example of a submarine from the same time period, visit the Museum of Science & Industry in Chicago, IL. There you can tour the U-505, a German submarine captured by American forces during World War II. The U-505 and its fellow Type IX U-boats were manufactured in 1935 and 1936.)