Questions about broadway stage door...

First of all, as someone who stage manages/works backstage for a living, this warmed my heart. Thank you so much for taking the time to appreciate folks like us! :)

As for getting an autograph, your best bet would be to write to them and ask for a signed playbill same as you would an actor; or try to get in touch with them via Instagram or email and let them know when you will be coming to the show. You can politely mention that you would love to chat at the stage door or get an autograph if they are able. Otherwise, you likely won't see them come out as we are usually some of the last to leave the theater!

I wish you luck with this and with following your ambition to be a stage manager in the future!

I would definitely recommend reaching out to them via social media to let them know when you're coming to the show and your desire to get their autograph and a quick hello. As others mentioned, stage management is often leaving well after everyone else, and if we are leaving while cast members are still signing we tend to power through the crowd as we aren't the ones people are usually out there to see. There's also the potential that certain members of the team aren't at that performance (such as if they were in rehearsals during the day and have a sub covering the performance that night) so it can't hurt to confirm that the person you're hoping to meet will be there that night.