Captain America's shield is made of Vibranium which came from Wakanda. Given Wakandan tech was so advanced and Wakanda was so protective about Vibranium, how could US government collect a chunk of Vibranium from Wakanda?
Here's some mentions of vibranium and Wakanda I could find in the films:
Howard Stark: Vibranium. It's stronger than steel and a third of the weight. It's completely vibration absorbent.
Steve Rogers: How come it's not a standard issue?
Howard Stark: That's the rarest metal on earth. What you're holding there? That's all we've got.
Tony Stark: If this guy got out of Wakanda with some of their trade goods...
Steve Rogers: I thought your father said he got the last of it?
Bruce Banner: I don't follow. What comes out of Wakanda? [looking at Steve's shield]
Tony Stark: The strongest metal on earth.
Ultron: ...Upon this rock I will build my church. Vibranium.
Ulysses Klaue: You know, it came at great personal cost. It's worth billions.
King T'Chaka: When stolen Wakandan vibranium was used to make a terrible weapon, we in Wakanda were forced to question our legacy...
Emphasis mine. From these quotes, two things seem clear:
Wakanda is known for having, and sometimes trading, vibranium.
Vibranium is believed to be extremely rare.
Based on these facts, it seems likely to me that the US government (or Howard Stark) simply bought the vibranium from Wakanda. Likely it cost a fortune, and the buyers were led to believe that they got absolutely all of it.
This was perhaps a diversionary tactic by the Wakandans to prevent invasion; once the secret got out that they had vibranium, foreign nations would take interest. Rather than destroying these foreign nations (and revealing their power to the rest of the world), Wakanda must have decided to take a more peaceful approach by pretending to sell off all their vibranium to the Americans.
The method by which Dr. MacLain obtained his sample of vibranium has not been divulged. It is also not specified if it in fact came from Wakanda - the term "Wakandan vibranium" is a description of the metal and its properties, not simply its source. It is referred to as "Wakandan" as that is its most common source; there are other, far smaller sources.
This is in comparison to Antarctic vibranium, which has almost entirely opposite properties to its Wakandan counterpart. Again, the name comes from its primary source.
In the early 1940's a small amount of Wakandan Vibranium came into the possession of the young, brilliant scientist Dr. Myron MacLain. Dr. MacLain began to develop super-strong metals for the US Government at the beginning of World War II. While experimenting on iron alloys for use as tank armor, he accidentally created the ultra-resilient Vibranium-iron alloy shield used by Captain America. Although he was never able to duplicate the alloy, after several decades of continued experiments, MacLain finally produced the formula for True Adamantium for the US Government