As far as I know, none of the original prototype Adolphe Sax saxophones have survived. I'm talking about the original ophicleide-shaped bass saxes made before 1850, not the normally (sort of) configured basses like the one at the American Music Museum. The first saxophone was almost certainly a bass in C or Bb. Most scholarly articles have said it was in C, but recently Howe has made a creditable argument that it was in Bb. Bass saxes in Adolphe Sax's earliest catalogs were in C.
When saxophones were entirely handmade in the 1800s, it was not so difficult to make a sax in an unusual key, nor was it much more expensive to do so. Adolphe Sax certainly had the knowledge to determine the necessary measurements. Also, very early original Sax instruments DO exist, including C sopranos, F altos, and C tenors.
Sax probably manufactured horns to meet the demand. There was certainly a demand for military instruments in Bb and Eb, because Sax was an official supplier to the army. Since the saxophone was an entirely new instrument, there was very little (or nothing perhaps) of any consequence written for saxes in symphony orchestras.
One thing that is often ignored is the music composed and published for saxophone when the instrument was first produced. Much of this music was published by Adolphe Sax himself. As far as I know ALL of the saxophone music commissioned and published by Adolphe Sax was for saxes in Bb and Eb, and it was classical music.
Berlioz mentions the saxophones in C and F in his treatise on instrumentation, and that may have led to more interest focused on saxes in C and F, both at that time and also later. However, the treatise was written so early in the saxophone's development (1844) that it would have been impossible for Berlioz to predict the future implementation of saxophones in the orchestra. Interestingly, Berlioz did NOT use saxophones in his compositions for symphony orchestra, although he was an important supporter of Adolphe Sax and wrote for smaller ensembles that used Sax's instruments.
I'm still hoping that somewhere, perhaps in a French or Belgian attic, an original Adolphe Sax prototype bass saxophone turns up, in good shape, whether it is in C or Bb.