The actor for Ozymandias has said he likes to develop backstories when he isn't provided one based on a suggestion Paul Newman made. Veidt is an Eastern European name and many wealthy Germans emigrated to America during or after the Second World War so it's not a huge stretch of the imagination that the Veidt family may have profited from the War or escaped the country before the economy fell to pieces. The actor put forward the idea to Snyder and he said he could run with it.
Besides, in a way it adds another layer to the story if Veidt was part of The Hitler Youth who used his upbringing, Captain Metropolis' chart of progress and his father's fortune to prevent the possibility of any further wars that would threaten his new home in the same way World War 2 forced him and his family out of their previous one. Also it's acknowledged that scientists and propaganda specialists from the Nazis were brought to America to work for the government and CIA, maybe Ozymandias used his connections to find out who they were, how he could use them to further his own empire after he retired from superheroism and how they could be used for his ultimate plan.