More than you would think, but focusing on this is something that people who aspire to build companies do to avoid actually building companies. You're almost always better off writing software or talking to users.
I know, but respectfully, one day spent on contacting people to get the word out is almost always a poorer use of time than figuring out what people want and building it. People, particularly people for whom it is their first rodeo, overestimate the impact of gatekeepers, PR, influencers, etc.
Who's the #1 person you could hope to get the word out in the world? Wave a magic wand and get them, and you'd probably find that this gets you zero additional users at the margin.
Publicity is a multiplier for product quality. Until your product quality is really high - as in, people are seeking out your product because their friends recommend it - the marginal benefit of publicity will be less than the marginal benefit of improving product quality. If you are at that point, you won't need publicity, though it can help accelerate your growth.
You are almost always better off talking to your existing users and getting their honest feedback about the product than trying to get a celebrity endorsement.
