Prior to 2010, I don't think I'd ever heard of the word. Somewhere around 2014, it started to show in columns or commentary of people....usually charged up on political objectives or 'revolution'.
So the basic meaning of this....you were going down some path in your life, with various perceptions, wisdom, and beliefs guiding you, then one day....you 'woke up'. The path is no longer valid, or walkable. You challenge yourself continually about what you see on TV, hear from politicians or journalists, and are in a continual state of either denial or disbelief.
Some folks will use the expression that you were deprogrammed, and now have a clear understanding of things. Other folks will say that you've been RE-programmed, and now have a misunderstood thinking process of things. Complicated? Yes.
So, could you have a woken-wokeness? That's where you suddenly realize that this whole perception you gained over the past year or two....is basically bogus, and you were fed a big long piece of BS? Well....yeah.