Employees are not able to view or enter information into the custom fields options.
But, you could have them enter a date into another info field such as the 2nd phone field. This way, they can enter it themselves and it will show in your Employees List (if you’re not currently showing that column you can click on ‘Select Columns’ near upper left).
add a field in the employee profile (my info) that the individual could go into to fill in a date