Gotta show value.
There’s certs out there that can help
If you haven’t worked for anyone in that role before I’d recommend trying to work for people in that role for a few years before striking out on your own.
It helps to have a bit of a network and some social proof that you know what you’re doing.
You could also start a blog and get it highly ranked on Google. That would be impressive to someone who would evaluate the ROI of hiring an outside SEO person vs hiring their own.
In general big companies, well paying ones, I would think would prefer to keep their SEO person in house