Not really sure how I came across this one but from what I've read, Mario's Big Adventure had two separate releases back in 1986. One was a promotional album given to Mario Fan Club members, called Mario's Big Adventure/GO GO MARIO!! and the other, which is called Mario's Big Adventure, may have been a promo as well but that I cannot enough information to be sure..
The albums were created on both cassette tape and vinyl record, sometimes you can catch one of them selling on ebay(albeit, somewhat costly). The only difference between the two of them is they have slightly different album covers—I included both in our upload—and for "Side B" one album has a song called "The Koopa Family's Counting Song" while the other has a song called "GO GO MARIO!!(arrangement of the overworld theme)" So, rather than create a separate downloadable album for only one song, I blended both of the albums together.
It was surprising to see that Nintendo was releasing promos so early on and even had a Mario Fan Club put together so long ago. Mario's Big Adventure Soundtrack is uploaded and you'll find it in the archive.