How does Howard Stark get the vibranium for it? Is there any MCU explanation for it? Or just left to wonder?
The origin isn't really explored in MCU.
However, there are a couple of origin stories offered in written works
While the origin and fate of the original shield were not described in the original comics from the 1940s, the shield's fate was revealed decades later in 2001 through a retconned story. According to the tale, King T'Chaka of the African nation Wakanda met Captain America in early 1941 and gave him a second sample of vibranium, an alien metal with unique vibration absorption properties and found only in Wakanda and the Savage Land. The new Vibranium sample was used to make Captain America's circular shield and his triangular one was retired.
In 2010, the history of the original shield was revised. In the limited series Captain America/Black Panther: Flags of Our Fathers, Captain America, Sergeant Nick Fury and the Howling Commandos meet Azzari (grandfather of T'Challa) -- the Black Panther and king of Wakanda during World War II. Aided by Wakandan military forces, they successfully repel a series of Nazi assaults led by the Red Skull and Baron Strucker. During the battle, the Red Skull (wearing a battle-suit) crushes the triangular shield, and Captain America uses a circular vibranium shield provided by T'Chaka to incapacitate the Skull. The weapon serves as the inspiration for the circular shield that the super-soldier begins using upon his return to America, and the encounter marks the beginning of friendly relations between the United States and Wakanda.