Last summer I had the opportunity to examine and even hold (but unfortunately not play) the very first Sousaphone, built by J. W. Pepper. However, I was not able to confirm the date that the horn was made, but only to narrow down the range of possible years to 1894-96 (as per various posts below).
But this past Spring I received word that appears to confirm that Pepper's Sousaphone was built in 1895. While I have not seen the actual document (yet!), I'm told that the following appears in Pepper's Musical Times and Band Journal, no. 155:
"In a letter dated October 14, 1895, Mr. Herman Conrad, the famous bass player of Sousa's Peerless Concert Band, writes as follows concerning the new instrument, the Sousaphone, which was made by J. W. Pepper, under Mr. Sousa's special instructions: 'The Sousaphone has become the talk of the town and gains in reputation daily. The Sousaphone is a splendid instrument. It is well in tune and has wonderful carrying power. The photographs of the Sousaphone are in the windows of one of the principal music stores on Olive Street (St. Louis), which is THE street of this city, and are a great attraction.'"
Curiously, as I noted in posts below, this horn doesn't seem to have received much press, and had essentially disappeared by 1898, at which time Conn's first Sousaphone got all of the attention - even to the point of assuming that their horn was the first!
[Thanks to Don Johnson, of the Kentucky Baroque Trumpets, for drawing my attention to the above quote. Don hopes to write a book someday on the history of the J. W. Pepper company - a book I would be eager to read! Get crackin', Don!]