A while ago there was a large data center outage that effected a lot of popular services and I speculated it might have been BGP, but it wasn't.

During that time I was trying to learn BGP on-the-fly enough to know if this was a thing and I didn't have a lot of luck.

What are some good methods or tools to know if BGP is causing a large scale outage before other experts have reported it?

https://radar.cloudflare.com/routing might be of interest for aggregated data that doesn't require a complete understanding of the internet. The global looking glass that bgp.tools has is pretty powerful too, but it gives you a lot of data, so if you don't know what you're looking for or what it should look like it's hard to say something is wrong.

Its usually not BGP, its some operator misconfiguring BGP, and there's loads of ways of doing that and its hard to know what that would look like from a remote view like your own network. Most efficient way is to just compare current bad state to previous good state and look at the diff, ie what changed for some prefix in your table compared to previous version of your table.