Except for the F1 > OPT > H1B > EB-3 and marriage route, is it possible to get sponsored for a green card by an employer directly?

I am currently looking into migrating to the USA long term, but as much as possible I really want to avoid having a financial downtime by doing a master's or PhD. My question is what experience is needed and what are some strategies in order to get sponsored for an immigrant VISA?

For context, I graduated Magna cum Laude from a Big 4 University. Got my thesis published. I have nearly 4 years of experience in web dev (React, TypeScript) in a corpo environment. I started remote work last year with a European employer and now currently working in a team in charge of the backend services with some frontend.

Would be happy to hear some stories too! :)