Seattle is a lofty goal, especially with how costly the city has become. I would suggest another nearby city with a slightly less obscene cost of living.
So Washington has all kinds of social support networks, but they're centered more in some bigger cities such as Seattle, Tacoma, Olympia, Everett, Vancouver, and Bellingham. The Eastern half of the state (divided from the West by the cascade mountains) is very rural and conservative, if not outright MAGA. These supports exist in the East but they're less robust and the cities are less welcoming.
What you should focus on is finding the cheapest city out of those listed above you can afford, and find a way to get work and to start putting money away for a place right away. Use all social services available to you, ask for a social worker at the Department of Health and Human services and they can help walk you through what resources are available to you. At least get on SNAP benefits in Washington if you can (requirements are a little looser out here than Louisiana, if I recall). Sign up for every program you qualify for, join every group that can help you network and get help.
The bad news is yeah, no matter which of these cities you live in, you're going to probably end up with roommates, as a studio can run in the $1200+ a month range.
The good news is all these cities are very warmly welcome to trans folks, queer folks, neurodivergent folks, as well as vegetarians and vegans.
Cities to Avoid: Anything West of Olympia on the peninsula. Anything East of the mountains.