In 1992 Bainbridge Records released Brass Menagerie: Big Band Brass of the Sixties, a selection of tracks from the catalogue of Time Records. Bainbridge re-released much of the output of Time, a label that was much favoured by stereophiles in the 1960s.
Brass Menagerie included tracks from the orchestras of Jerry Fielding, Jim Tyler, Hugo Montenegro and Mel Davis. One of the selections from the Davis band was Gonna Build a Mountain, from the Anthony Newley/Leslie Bricusse musical Stop the World, I Want to Get Off. Davis, a trumpeter who spent much of his working life in New York recording studios, had included the song on his 1963 Time album We Like Broadway.
Grab Mel Davis's Gonna Build a Mountain from the link below. The MP3 is sourced from a cassette version of Brass Menagerie.
Gonna Build a Mountain
Brass Menagerie appears to be available on CD from a few sources, including the iOldies Music Store. The album is also available as a download from most of the major sources.
Mel Davis accompanied Benny Goodman on a 1957 trip to Japan and here's a wonderful YouTube video of Air Mail Special from that tour. Cue in about 1:05 to bypass the lengthy drum solo that opens the clip if you prefer. Davis is up front beside Goodman.