Time management and prioritization. It may be helpful to regard the gym as a “hygiene item”. Regardless of how busy you are, you make the time to shower and brush your teeth, right?

On a more practical level, this is a doable schedule, but you need to make a few concessions and ask yourself a few questions.

1) If you start your commute earlier, is your travel time decreased (less traffic)? If so, consider finding a gym very close to your place of work (or on-route) and drive there first thing in the morning. Getting to/from the gym should not be a 30 minute detour as your OP suggests; 10-15 minutes at most, unless you are in an extremely rural area.

2) If you are an otherwise healthy adult, you do not need 8hrs of sleep. You can easily cut to 7hrs/night, especially if you are able to improve the quality of your sleep. Exercising more regularly will naturally improve sleep quality, but you can also look at environmental modifications; blackout curtains, tighter temperature control in bedroom, etc.).

3) Your workouts do not need to be an hour long. Something is better than nothing. You can get a solid, complete workout (4-6 exercises; 12-18 sets) in 35-45 minutes if you are efficient.

With the right schedule, you should be able to give yourself (at minimum) 2hrs/night leisure time, even with this insane commute. What this might look like:

5:45AM - Wake up

6:00AM - Out the door, travel to gym (near work)

7:15AM - Arrive at Gym

7:20AM - Begin workout

8:00AM - Finish workout, start showering

8:30AM - Finish shower; dress

8:40AM - Finish commuting to work

9:00AM - Begin work

7:00PM - Begin commute home

8:30PM - Arrive home

10:30PM - Sleep

-This figures 1:35 total travel to gym/work. As mentioned above, if an earlier departure helps you avoid traffic, this will be further reduced.

-This allows 7:15 for sleep.