Neither the I-94 nor the FOIA requesting the entries/exits contain the time of the day: they only contain the dates. Where can I find the time of the day of my entries and exits to/from the United States?
Regardless of whether or not such a website exists, relying on using their timestamps is a bad move. The general rule is that if time of the day matters, assume it’s the least favorable time for whatever immigration purposes you have. You don’t want to argue over time zones or hours worth of differences with a faceless bureaucrat who’s happy to reject your application or deny you entry.