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: