Truth is, it’s difficult, but it can be done. Many, if not most, writers shoehorn their prose between a primary job, the laundry, and driving the kids to soccer practice.
First, remember that you’re after a rough draft, not a finished draft. Rough = bad. Ask yourself, Is one hour a day enough time to write a bad first draft of a chapter? Probably it is. As someone once told me, “Don’t get it right, get it written.”
The more you write, the better you will become at writing better first drafts, but they will always be rough. You must give yourself permission to write badly.
Second, don’t try to write a complete (as in fleshed-out) first chapter. Instead, write a skeletal first chapter with the main action and the main dialogue in black and white. To do this, sit down and imagine what you see and hear as you live the events of the story. Try to capture conflict and unexpected details through the senses (what your hero sees, hears, feels, tastes smells—and thinks.)
Third, find a pace that matches your time. If you can only put five hours into the rough draft of each chapter, then pare down what you put onto paper so that you are writing 20% of the chapter every day.
Sure it will feel rough and incomplete. Yes, you will probably hate it, and it will take practice learning to discipline yourself in this way. But when you are done you will have something to work with that can be revised. And I think you will find that the story is more compelling—even in this skeletal stage—than you thought it would be. If it isn’t, then no amount of fleshing out will fix it, and your problem isn’t one of time, but of a flawed story. In which case the less time you spend on it, the better.