I assume you're asking about the release of recordings of music?

Oh no, Bing Crosby was far from the first. Sound recordings, when they first came out, did not use a microphone for recording. Instead, recordings were done with the phonograph, initially invented by Thomas Edison. With these initial machines, one turned the crank on the phonograph, then played/sang/said whatever you wanted recorded into a horn like device attached to the phonograph. This sound was transferred onto the recording medium and could be played back but running the needle attached to the phonograph through the device. An example of this is seen here, with a small orchestra recording into one of these machines.

In the early days, these recordings were stored on Edison Cylinders made of wax, but eventually, the convenience of having flat discs brought an end to the cylinders.

So, to answer your question, yes, music was recorded well before the invention of the microphone, as Edison's Phonograph came out before the end of the 19th century, both instrumental and choral. If you'd like, I found that the University of California, Santa Barbara's Preservation & Digitization project has several cylinder recordings that they have digitized here. Not all of them have been that are listed, but a good many are.

I hope that helps you out a little bit!

Most of the early recording singers needed powerful voices, because this sort of mechanical "mic" needed strong vibrations to drive it. In fact, this led to the amplification of instruments, like the resonator violin, a violin with the resonating body cut away and amplification provided by a brass or aluminum horn.

The invention of the electrical microphone resulted in the rise of the crooners, men who sang in a soft, intimate style, like Whispering Jack Smith or the first multi-media star with screaming and fainting fan-girls, Rudy Vallée. Der Bingle broke later, and Russ Columbo shortly after.