Is there a problem with hiding "forgot password" until it’s needed?

To be honest, I don't really see any use for the "forgot password" button/link unless the user put in a wrong password before. In my current project, we need as much space as possible and I was thinking about showing it only when needed. My colleague talked about "Accessibility"-reasons why it is not possible, but also couldn't give me a real argument.

What is your take on it?