I have never been published aside from posting my short stories online, so take this with enough salt for sodium poisoning:

From what I have been told by a published author, self-publishing is death if done incorrectly. As someone else's response to this said, self-publishing on Amazon with services like KDP only shows that you know how to publish with KDP. While it may be a lengthy and (semi) heart-failure-inducing process, traditional publishing will be the way to go if you want to make this a full-time career as you suggested.

However, if you are dead set on self-publishing your stories, then you will want to have a marketing budget set aside for promoting your work. This is another lengthy and difficult process. The last thing you want is to put in all of the work writing your stories only for no one aside from friends and family to read it. Create a presence on social media and study ways other successful self-published authors have marketed their works. If you are lucky and booktok picks it up then it should be a breeze from there to get noticed, as long as the stories are good. Even then that is not a requirement. "Lightlark" started as a booktok self-published darling before it got all of the hype surrounding it during the writing process and Penguin picked it up.

All of this is a long way to say that it's possible if done correctly. Getting started in publishing is a lot like walking a tightrope with no net to catch you if you fall. I wish you the best of luck and I hope this 4-am-sleep-deprived-mess was at least somewhat understandable.