The first stage is the D-Day landings at Normandy.
While the console versions start on this stage and it is Allied Assault's most distinctive, the original PC version actually has two stages before the D-Day landing stage.
Lies about Medal of Honor: Airborne[]
There was an Allied parachute raid that targeted a German flak tower in real life WWII history.
This is a fictionalization on the part of the developers; even entire Soviet armies avoided these gigantic concrete fortresses, and such an assault would be outright suicidal.