What is causing the record to enter that view? If it’s a change to a field, you could add a last modified time field that only targets that field, which will give you the precise date and time. The only downside is that if the triggering field is changed elsewhere in your process, that last modified time will change also. If you want to keep that time for later review, you could use an automation—triggered when the record enters the view—to copy the date from the last modified time field to a static date field.
