With regard to the timeline in the framework and the Avengers, it seems to me (though I might be mistaken on this) that the Bahrain incident happened before Captain America was found (which I think happened in 2011).
In the framework, May did not kill the inhuman girl, she went on to kill many people in England IIRC, and that was the excuse that Hydra needed to attack and take over. As a result, SHIELD probably did not find Captain America, because SHIELD no longer existed. Hydra found Captain America, if anyone did. They probably have him locked in a box, experimenting on him, if he's still alive.
As for Thor, it's not clear that he would ever come to Earth in the framework. Running a simulation that simulates the whole planet is difficult enough. But simulating civilizations on other planets as well would take more computing power and information that probably isn't even available, and would be of no use to Aida anyway. She may well not have made Thor come to Earth. Alternatively, if Thor came to Earth in the framework, he would have been captured not by SHIELD, but by HYDRA. His chances would not be good.
Stark would not have stood much of a chance under HYDRA, either. He couldn't keep his identity a secret, so even if he managed to develop the Iron Man suit, the government (i.e., HYDRA) would have gone after him (and everyone he cared about), arrested him, and took the technology for themselves.
As for Black Widow and Hawkeye, they have no powers. They would have fought HYDRA, but would have been killed eventually.
The Hulk could do a lot of damage and kill many agents, but in the end, he probably would have been brought down one way or another - or else, Aida would have used her god-like powers in the framework to change things and get rid of him. She does not control everything that happens, but on specific occasions, she can intervene in that way (e.g., she rebuilt Jemma's body, apparently in order to track them).