There was a comic Scott Kollins drew, I think it was called Earth's Mightiest Heroes,
Where it retells the founding of the Avengers. Cap is revived and helps the team but he seems plagued by some secret demons from his past. The first bad guys they fight aren't Cap baddies, but eventually they do face Zemo, who Cap reveals killed Bucky and tried to kill him too.
So the first film can revive Captain America, and have him join the team, and not have the Avengers fight a Cap bad guy...
but it could turn out like the first X-Men movie (with Wolverine hogging the spot light). Cap might end up being the central character and taking up more screen time and plot time than the others.
And pehaps the studio might do this and then think to use a Captain America bad guy and make all three Avengers movies Cap movies co-staring the Avengers.
Just saying its possible.
I say make the first Captain America movie mostly based in the past, then maybe have him get frozen at the end. This could set up Cap's world for a whole 2 hour movie, a world during WWII. Set up his friends, his partner "Bucky" Barnes, set up his origin and his character, then freeze him at the end.
As part of a secret ending of say Iron Man 2 (or after the credits of Captain America, if so we cut to present time) we see Tony Stark and some explorers find Captain America frozen. End.
Then in the first Avengers' film make Cap's story just one of the stories so that it doesn't take center stage, sort of like a side story or a sub plot.
Cap's inner turmoil and displacement in time wouldn't have to take up the film.
The Avengers (first film anyway) should be about five different super heroes coming together, not just about one in particular. Not yet anyway.