First, when did a chicken genetically become a chicken? you could simultaneously build your product and your customers at the same time. Take a general idea and use your customers who are interested in the broad idea to bounce ideas off of and build the product around them and adapt further once things become more polished. Have your chicken and egg a the same time. =)
Completely agree with your statement "Take a general...". Most often though, people run off to build a product even before they spoken to anyone ourside of their close family even excluding friends sometimes. Then you have a product and no users let alone customers.