First, VSA is short for Vereinigte Staaten von Amerika!
It's a rare abbreviation, but it exists/existed.
I have mostly seen it in publications from the Social Sciences and always asked myself, if this VSA had been imposed by a very old supervisor, some rules requiring usage of the German language or if it was the author's free choice.
(In a comment to a deleted answer the usage of "VSA" is attributed to ein paar rechte Spinner. However, my samples were mostly from politically left-leaning sources.)
USA is infinitely more common. There is a normative power of the visuals as Christian Geiselmann calls it. If you see "USA" printed on every bag of food aid, on every second T-shirt, on vehicles around military bases, in TV news broadcasts about US politics and so on, then it will become natural. (It might be different, if people don't speak English and use a different alphabet.)
What's about UK? That abbreviation is widely understood, but rarely used in German. If one wants to shorten "Vereinigtes Königreich von Großbritannien und Nordirland", one uses Großbritannien, England or GB. I don't remember having ever seen UK in Germany, whilst GB is often seen on the streets (on every British car). GB is also more common as label in statistical figures accompanying newspaper articles.
One important factor: The abbreviation UK hadn't been terribly popular in the United Kingdom either. Its usage didn't gain steam until the mid-90s (see Google ngram).