Currently always defaults to 08:00 AM, is it possible to adjust this time to always say something like 06:00, for instance?
To customize the snooze times go to Google Keep in the same account, open Settings (gear icon at the top right), and edit the times from there. Verified working with G Suite as well. Make sure to reopen your Gmail tab after saving the settings.
So from Inbox:
Result, affected both Inbox and Gmail:
I also had this problem, and found that changing the settings in the Gmail app on my iPhone updated it online too:
Your Account → Snooze settings and editing the times in there!
Nowhere to be seen on Gmail.com, but the settings pulled across.