Brief answer for those in a hurry:
Give yourself treats when writing. Condition yourself to feel that pleasure when you write. Find some passive inducing activity that gives you pleasure and associate it with writing.
Long answer for the details:
As a craft, there are many ways you can approach writing. But like any craft, you can only get better at it by doing it. Thinking about it won't get you there. So you're right. Write things down. Write them unfiltered. That's a start.
Now, like any other craft, you may start having more fun the craftier you get at it. And to get craftier you have to write. So here's my trick to kick start the process.
I like music. I like music a lot. Music is sweet. And like all sweet things, I can only take so much of it before it starts to become too much (dopamine depletion). So I decided I had to go for a diet. What if I only listen to music, and the music I really like, when I write?
That's what I have been doing. For more than a year now, I only listen to music when I write. Like a well trained pet, this has triggered a conditioned behavior. Now, whenever I feel like hearing music, I also feel an urge to write. Sometimes I hear a song playing somewhere, and I'm reminded of things I want to write.
Funny how this goes. As of now, I'm finding pleasure in writing qua writing. In a way, I feel I'm starting to ride this craft no longer needing those musical training wheels. But since I always have music at hand, I always feel safe. If I'm assigned a writing task that I'm not particularly fond of, I turn the music on and the task becomes a bliss.