Is it actually possible to do something without motivation?


You can force yourself. The world at large does this in so many areas. Many people lack motivation, that find their way to work everyday.
But if you find yourself lacking the motivation to actually complete a goal, start off small, try to establish some habits. If you can't bring yourself to type an email at your desk, then step one is sit at the desk, step two is to open the laptop. Doing the very simple next step can help in getting hard stuff done, when u dont feel motivated.

I once fell out of a tree without having any motivation to do so. In fact, I was quite seriously motivated about not falling out of that tree. It didn't help.