I mean, you can easily find thousands of hours of music online. Recording background noise is easy (just go to a random bar where they are not playing music). Now simply add the two signals (you can shift them randomly to generate more data). You can also add some linear filtering if you like (just imagine random settings of an equalizer for starters).
This should give you enough data to build a proof of concept at least.
Illegally grabbing thousands of hours of music to train a commercial model hardly qualifies as fair use. Any company you build upon that would be tainted.
For sustaining:
In addition, you'll need to keep an updated catalog of music to identify new songs against, and most uses of a service like shazam are to find names of songs people aren't familiar with, so that catalog needs to be very fresh.
That means you'll have to grab some sort of feed, and engage in large scale music piracy for commercial gain or have access to a library of songs from many disparate music providers, such as ascap.
Background noise:
there are literally hundreds of different background noise environments you need to train against. Dozens of common microphone configurations. Clipping, variations.
It's very much a problem where a proof of concept is neat but doesn't really get you anywhere.
