Yes, you can enter the Going-to-the-Sun Road from West Glacier before 6 AM or after 3 PM without a reservation. Do note that 1000+ reservations for any particular day are opened up the evening before; this is how we managed to get tickets at the last minute and make this video.

I went in late June 2024. We did have reservations, but we didn't actually arrive at the west entrance until right at 3pm, so we didn't need them. We drove all the way to Logan Pass, with a couple stops early on. We didn't go back down on the east side, instead we turned around at the top and went back down the same way. At that time, the sun doesn't really set until after 10, so my friends and I were back in Kalispell for dinner at 8:30. We didn't do any hiking or anything, so it was more of a scenic adventure. Just after we turned around at the top, the road was kind of blocked by a half dozen or so big horn sheep that were walking, so everyone stopped and gave them right of way. It was amazing.