Be bold and brave and see which theatres bite once you send out your resume.
Not only is being a union member a must for working on Broadway, but it can be your opening to higher-paying work, as well as protection against workplace mistreatment/injury and great long-term benefits such as health insurance and money for retirement.
The Broadway touring shows that travel from city to city all use union stagehands who are based in the local city in which the show is playing.
Once you are a member (and in some cases, registered), you can start to look for work on the Great White Way.
Broadway job openings aren’t really announced, so you have to be smart and have some strategy when getting your resume out there.