In practice, it works this way:
Customer #1: Yes, you are the first customer. I'll give you the product for 90%, it's a great deal
Customer #2: We have customers. For instance, see customer #1. Pay full price.
Customers are usually not stupid. Giving away the farm to the first buyer is a wise investment and the price to pay to start a business. You can fight to avoid it, or just get it over with.
Focus on how many people have used your product or service (some may not have only tested).
Mention any background you or others in your company have had with similar products/industry. If one of the Google guys left and created their own search engine, even if I was the first person to try it, I'd bet it would be pretty good.
Show them the benefits of doing business with a startup.
Using our contacts, try to pick a decently famous company ( it can even be a startup - like Dropbox for eg;). Get them on as your customer. Companies like them would usually not take time to say a yes / no since they are small (but popular, that's the key!).
Once you have a company like that as your client, you could talk to more people and say - we have Customer 1 and are talking to a lot of companies like Customer 2, Customer 3, etc. [ nope this isn;t a lie - you are indeed having a conversation with them]
That's enough - it would catch the attention. The point is, most big companies would like to hear a few popular names before signing up, this is the last step to close the sales cycle.
Number one thing you should do is go out and find someone you can give you product to for free or at a highly discounted rate (mentioned above).
This will allow you to test the product and get good ideas of what your industry is looking for. A big mistake developers make is that they design a software that they would use, which most times NOT what the mainstream will want to use.