put, no. In the comic books the first five Avengers were Iron Man, Thor, Hulk, Wasp, and Ant-Man. Captain America did not show up on the team until the fourth issue. Yet Steve Rogers appeared in comics much earlier back in 1941.
Steve Rogers was created from Timely Comics (the predecessor to Marvel) in March 1941. Rogers was a scrawny guy who wanted to fight for his country. Rogers was injected with the super solider serum, and he became Captain America. Captain America was intentionally created as a means to fight the axis powers during World War II in the comic book world. Captain America was meant to be a tool to help young boys find patriotism within the war effort. When the war ended Captain America's popularity faded and he disappeared during the 1950s. Like within the film world Captain America was "thawed" and joined the Avengers; he stayed (Steve Rogers) stayed a part of the team and even lead the team. In 2007 Steve Rogers was killed, and his friend Bucky Rogers took up his costume. Steve Rogers eventually came back to life, and now is in charge of S.H.I.E.LD. When Bucky died recently he took back his costume.
In the film world Captain America aka Steve Rogers is played by Chris Evans. While I was skeptical about the casting in the beginning Evans had incredible charm, and played the role with great conviction. In the film we get to see the early days of Steve Rogers, the birth of the costume, and the hero himself. Captain America also faces his arch nemesis the Red Skull or Johann Schmidt. The Red Skull is the successor to Hitler and like within the comics represents the evils of Nazism.
Steve Rogers may not have been the First Avenger (exactly), but he certainly represents everything this group stands for, and is a true representation. Captain America is the eternal good guy; he is tough, strong, and as his name represents he is the all-American hero, who fights against the evils of the Marvel world.