Not really. That's pretty much hardwired into FileMaker date fields.
You might, however, use a text field for data entry with a date field that auto-enters the text of this field as a date with this auto-enter calculation:
GetAsDate ( YourTextFieldHere )
You can then use validation calculations on the text field or a script performed by OnObjectValidate to check for data entry errors such as an omitted date or incorrect formatting.