So DNA didn't store any information until a conscious human learned how to read it?

It didn't. DNA is simply a complex structure, which, placed within another complex structure (a cell, containing appropriate amino acids), creates further complex structures (proteins).

  Otherwise, how could consciousness have evolved in the first place?

I don't know. However, I disagree that information needs to be an independent physical property for consciousness to evolve.

The steelman [1] version of your view, I guess, would be that "information" is equivalent to "complexity". Certainly consciousness relies on complexity, but it's not equivalent. Hurricanes are very complex, but certainly not conscious. Some say that complex systems like waterfalls and hurricanes perform complex information processing, but I think this is wrong.

There's a fundamental difference between a human processing information (say, a bronze age man reading about metallurgy from a wax tablet and using the knowledge to craft a sword) and the actions of DNA, or hurricanes, or waterfalls.

[1] https://wiki.lesswrong.com/wiki/Steel_man