With literally $0 (assuming you don't value your time), you could try to find prospects and call them or email them or visit them and get them to sign up as users. This is, of course, totally unscalable and unsustainable if you want to sign up millions of users. But it's actually how lots of companies get their first 100 users or so in order to prove that their service or product has value for a specific category of people.
It all depends on what you are selling, and what you hope to achieve in terms of "user growth". If you are hoping to sign up millions of consumers to use your app with $0 in marketing -- yeah, prolly not gonna happen. If you have a B2B SaaS service and you can define your target prospects, there are some very low cost ways to generate targeted leads, and if you can convert those leads to customers you can bring in investors.
Sam, this is part of what I do every day for numerous research teams at University of Washington. Check out my linked profile and if you think I can help you let's chat: www.linked.com/in/misterrobinson