Making your own groups is surprisingly effective.
I know, you probably don’t want to do it, but that’s why it’s effective: a lot of people feel that way, they want to hop in an existing pug group.
Concretely, that means that it’s much easier for you to complete a group that you start than it is for you to be chosen as dps in somebody else’s group.
Finding a tank might be a struggle, but it frequently is regardless. As long as you are not so under-geared as to be a complete carry, it’s usually the fastest way.