When you start out I’ll assume you have nothing, but the reality is if you’re starting to DJ or interested in DJing in your Tango community, people have music and are always offering to share. You also should be hearing a lot of music at the different classes, practicas, and milongas. Many teachers will even mention who the music is by in the class, and you can always ask if you are unsure and even get song names. If they don’t or some other reason prevents the conversation, apps like Shazam easily identify most popular tango songs.
You may also notice as you’ve been dancing, there are many popular songs, artists, singers, and there are patterns. Depending on your community there may be different structures, but they are all very similar. A pattern will arise that you’ll start to hear the same songs over and over again, it might give you a stale feeling at first, but there are reasons. In tango, there are thousands of songs, but many songs are done multiple times by different artists, singers, years and orchestra compositions. These are the popular songs, the ones that people know and love dancing to, and overtime you have your favorites and you look forward to them. So you don’t really need 10,000 songs in your collection, starting out, you can only have a couple hundred.
So if you’re starting out, you should start by identifying the popular songs, artists, singers, etc and build from there. Start small, you can find most on any popular platform, and once you get some good names, start listening to more from them. A good 10-15 songs from artists like Canaro, Di Sarli, D’Arienzo, and Troilo can get you started.