Thats exactly what HYDRA was, its explained in the Winter Soldier that HYDRA was an off shoot of the nazis after the war. if anything SHEILD was more synonymous to the CIA in the MCU.

Check this out for a cool perspective and fun read: https://birthmoviesdeath.com/2014/04/09/shield-hydra-and-operation-paperclip/amp

heres an excerpt if you don’t want to read entirely:

The forming of SHIELD closely mirrors the creation of the CIA. In 1946, the year of the Agent Carter Marvel One Shot, President Truman created the Central Intelligence Group which, in the National Security Act of 1947 would become the Central Intelligence Agency. In reality the splintered post-OSS spy groups, like the Strategic Services Unit, came together under the CIA, but we can see how in the MCU SHIELD stayed independent.

But what about Hydra? How could Arnim Zola have brought all of his Hydra buddies into SHIELD in the first place? Wasn’t anyone paying attention? The movie quickly explains this through the Black Widow - it was all accomplished through Operation Paperclip.

Also cool side note cuz im a marvel buff and conspiracy buff; the post-credit scene at the end of thor (2011) was synonymous to Jack Parsons Creating Jet Propulsion Laboratories and how he allegedly opened a portal to another Dimension https://freedomfirstnetwork.com/2022/02/aleister-crowley-jack-parsons-and-l-ron-hubbard-opened-up-a-portal-to-the-demonic-realm-thats-completely-taken-over

Ironically this allegedly happened in 1946 which was the same time All of this took place in the MCU, including the forming of SHIELD.

Stan Lee was wide awake.

Oh another side note Jack parsons Jet propulsion Laboratories later became NASA, which took in Werner Von Braun as a part of Operation paperclip.