What are some ways for someone to become a successful author without being part of a publishing house or literary agency?

When it comes to writing you have to start somewhere. It's not a hundred percent guarantee that you'll become a successful author just because you joined a publishing house or a literally agent.

Personally, I think you should first start writing some short works and post it, so that you could gain some audience. With you practicing more and more while putting yourself out there, you'll be able to discover and learn a lot of stuff i.e; the writing style fit for you, more expressive vocabulary etc.

With this you'll also have gained some fans and a publishing company might like your work and reach out to you. So you should try publishing your works on apps like; Wattpad, Novelbin etc. to get more exposure.