Shield didn’t exist yet when the Super Soldier Serum was created - it was formed after WWII. Hydra was infiltrating other organizations before that - the spy who tries to sabotage the creation of Captain America, for example - but not to the extent that they were later able to compromise Shield.
Shield itself was apparently compromised from the beginning. After the war, when Shield was being formed, they brought in “ex” Hydra agents who had valuable knowledge like Armin Zola, Operation Paperclip style. Presumably, it took some time for these agents to exert control over enough of the organization that they could pull the coup we saw in Winter Soldier.
When you ask how obvious it was, I’m not sure what context you’re asking in. Do you mean “How obvious was it to the characters in the story?” Or “How obvious was it to the audience at the time?” Although, in both cases, I think the answer is “not very.” Nick Fury, arguably the best spy in the world, only had vague suspicions that something was off in his organization, and I don’t recall any hints dropped in previous movies to suggest that such a betrayal was in the cards.
After the events of Winter Soldier, Shield was officially disavowed and defunded. At the end of Age of Ultron, a heli-carrier showed up to help evacuate Sokovia, which was established in the TV show Agents of Shield as being the results of Shield reforming and getting it’s shit together, but the show is mostly non-canon, so it’s not clear if that was still supposed to be Shield, or what. The end credits scene on Captain Marvel showed that Nick Fury is running a new operation, apparently in outer space. This is likely Sword, a counterpart to Shield from the comics that focuses on extra-terrestrial threats.
The MCU seems largely finished with Hydra as a major threat, so I think it’s safe to assume that they’ve not infiltrated Fury’s new org.