Self-improvement takes change and effort. It requires an investment of energy larger than the one required to overcome life's usual busyness. If you really want to write a novel, you will write it, even if you have to burn sleep to do it, even if you have to get it done by spending your days daydreaming about the plot and your evenings furiously typing. Plenty of works of art were created in this way. If you really want to learn a new skill, you will learn it -- perhaps not as
well as if you could focus on it, but bits and pieces here and there, a podcast on a drive, a few rounds of practice over lunch. Plenty of people have mastered life-changing skills while holding down the proverbial two jobs with three kids.
It is possible to be so busy that this is really what holds you back. But very few life situations outside of the gulags are really so grueling that work is really able to squeeze your free capacity down to nothing. It is like wanting to go to space, and being intimidated by having to drive over a hill. It is possible for a very high hill to be a practical problem, but if an ordinary one looks insurmountable to you, you very likely never had the energy to go to space.
That's not to say you never need to quit a job to give an extraordinary venture your full attention. It's more to say that if you are doing nothing right now, if you tell yourself work is the problem, work almost certainly isn't the problem. If you have the drive to do something once you have more free time, you'd be doing something with your free time right now. You wouldn't be able to not. Don't wait; start now. Can't? There's your problem.
I have noticed, with myself, this scales right down to tasks that literally take one minute to do, like loading the dishwasher. If my energy is high, I do it almost without thinking, while I'm waiting for water to boil, while I'm thawing hamburger. No big deal. If my energy is low, I don't do it at all, and I spend those same minutes staring at the floor. I tell myself I don't take care of the house because I don't have time, but as a lot of people found out during COVID, that was never the problem. I didn't have the drive. Free time turns out to matter, once I get going and want to do big things. But it matters little if I can't do little things that take no time.