I thought that SHIELD was a brand new organization at the time of Iron Man 1? Because Coulson didn't even have the acronym for it yet?
Actually, no. When he named the organization to Pepper, she said it was quite a mouthful and he said "I know. We're working on it." Then later, on hearing it again, Stark said "you really need a new name for that" and Coulson said "Yeah, I hear that a lot."
Maybe what you're thinking of is that he gave the full name a couple of times before finally giving in and saying "Just call us SHIELD." But I don't think it makes sense to assume that he was the first person ever to coin that acronym, because, as Agent Ward pointed out in the series pilot, you don't give an organization a name like "Strategic Homeland Intervention, Enforcement and Logistics Division" unless you really want its initials to spell out "SHIELD." So there's really nothing in
Iron Man to suggest it's a new organization -- just one that hadn't previously come to Tony and Pepper's attention. Perhaps it had maintained a lower profile before the emergence of people like Iron Man, the Hulk, Thor, and Captain America compelled it to act more openly.
I figured Steve Roger's gang was considered an immediate precursor of Shield with the military guys and the support from Stark's science branch.
Yes. As Simmons said here, the SHIELD Science Academy was originally the SSR Academy. The SSR was the group that Howard Stark, Peggy Carter, and Tommy Lee Jones's general character were working for in
The First Avenger. They were the direct ancestor of SHIELD, in much the way that the OSS was the precursor of the CIA.