When I first graduated from undergrad, I had awesome dreams of Grad school (and I was specifically looking at Columbia). The biggest points of interest for me were the exposure to multiple genres (including dance which I was not very familiar with), the focused curriculum (as my undergrad was a generic BA, with moderate tech education), and the opportunities for networking with some big names in the industry. As a young, recent grad, the networking was the biggest point for me. I thought it would be an easy-in to the New York industry and would amount to instant success.
But it turned out I wasn't able to start grad school immediately after undergrad because I was working at a summerstock that ran through most of September. So I thought, "well, I'll apply next year..."
And then I worked for a year in New York, and realized: I am my own networking capacity. I am perfectly capable of meeting, working with, and earning the trust of more experienced Stage Managers. I don't need to be force-fed to a professor who happens to be a Broadway vet (alongside several other SMs each year, and after who knows how many years of teaching).
Pretty quickly, what you can do is what gets you the next job.
juliec puts it as succinctly as it can get. Be a hard working, skilled SM, and people will notice. They'll tell their friends, and eventually the 'right' person will notice, and you'll land that dream job.
Or at least, you'll work. And that's a dream job in itself, right?