Conversion optimization is valuable and most businesses are happy to pay for a bump in new customers. What's your pitch? What's your web site? A whitepaper, or a web page showing what you can do will go a long way to demonstrating value to possible customers.
It's going to take a while to build a strong customer base and network that can keep you busy and in money. And it may be a month or more before you land your first client. That's OK. Any business requires you to stick with it, if it's ever going to have a chance to succeed.
But don't undersell yourself or take on a subpar client just to close a sale. It's far better to spend your time building your network and looking for serious clients than wasting time with a difficult client. A serious client will pay you upfront, usually a deposit of 50%, though sometimes less with a more detailed payment schedule. Any asshole can ask you to work on contingency. A deposit ensures that even if a client ends up being an asshole at least they're an asshole with money.