When starting a new habit you can't just add that to your day. Like it or not you are already doing something for the whole 24 hours per day. You can't just decide to start writing 20 minutes every day. You don't magically get 24 hours and 20 minutes per day. You need to find the time. Find something you do that is not important, productive. You need to quit something.
There are no moment in your day when you don't do anything. There might be moments wen you do nothing. There is the difference. Doing nothing can be important. More important is to recognize the moments when you are doing something that is just a waste of time. Quit those!
Quiting can be as hard as starting. But they go well hand in hand. You need to find time to start something, you also need to fill the time if you are quitting something. If you have something you really want to stop doing this is a good opportunity. Otherwise you just need to prioritize what you want to do.
So how did I find time for my writing? What did I quit? I have a morning routine where I spent 20 minutes reading news while waiting my coffee cools down. Perfect moment for writing. I have plenty of time later to catch up with news anyway.