Go to the Tools menu, Calendar options, and set the default start time to
04:00. Now when you enter a task date without including a time, it will
default to 04:00. Please note that setting the calendar to 24 hours is
usually a problematic situation. Setting a project calendar of 24 hours
means that when a task starts it will proceed 24/7 until it's done. Since in
a proper WBS the tasks are broken down to one task - one resource, that
means that tasks, once started, proceed 24/7with the assigned resource never
taking a break, having a meal, sleeping, seeing the spouse and kids, etc.
Machines work like that but people usually don't. It's far better to have
the project calendar reflect the typical work schedule of a generic
resource, IMHO.