The best time to leave on a long road trip is early in the morning such as by 5:00 AM so that you can get some miles in before daylight.
When I leave out on a road trip I pack the night before and if I have my camper trailer with me I have it all hitched up and ready to go the night before.
Then all I have to do is make my coffee in the morning and a bit of breakfast to take with me and then I hit the road by 5:00 AM.
That allows me a few hours of driving in the dark before daylight.
I'm usually awake by 5:00 AM anyway so I'm ready to hit the road by then.
I then drive for around 250 miles to 300 miles at most and then pull off and rest in my camper or in a motel.
Then I drive again early in by checkout time around 9:00 AM and finish the miles on the road trip.
Most road trips I take are between 500 miles to 1000 miles one way so I get the most driving in the first day and then the next day I drive more when possible.
So try to leave as early as possible to get out on the road and get some miles in.
You should drive no longer than 800 miles on a road trip in one day for safety because driving long distances can get very hard on you and make you really tired.