You do not have a free hour. You are not going to get one. The good news is that an hour was never the requirement — it is just the unit everyone quotes, and it is the reason most busy people quit before they start.
Shrink the session until it survives a bad day
Decide what you will do on your worst day, not your best one. Five minutes of speaking is a real session. A day you skip entirely is what actually costs you. The point of the tiny version is not the five minutes. It is that the habit never breaks, so there is nothing to restart.
Use the minutes you already waste
Commutes, queues, walking to the shop, waiting for something to load. These are dead minutes you will spend anyway, and most of them allow listening or speaking aloud. Attach the language to something you already do every day. The trigger matters more than the intention.
Cut the parts that feel productive but are not
Reorganising your notes, browsing method videos, comparing apps and reading about learning are all comfortable and none of them are practice. On a tight schedule they are the first thing to go. If you have fifteen minutes, spend all fifteen producing language. Preparation is a luxury of people with spare time.
Accept a slower curve without accepting zero
Ten minutes a day will get you there later than an hour a day. It will also get you there, which an abandoned hour-a-day plan will not. Compare yourself with the version of you who did nothing this year, not with someone on a sabbatical.
The constraint is not your day. It is the size of the session you think counts. Make it small enough to be unskippable and the schedule stops being the problem.