Excel stores such date entries as text instead of date values.  That becomes a problem if you want to format their appearances.  If users typed in 7/4/1776, 7-4-1776, 07/04/1776, etc., you want to format them all in a standard fashion.  But Excel doesn't see them as valid date values, so you can't convert them to, say, "July 4 1776".  One trick is to force it to become a valid date -- by adding, say, 1000 years to the year.  See the picture below as an example.  Extract the month and day, extract the year, add 1000 to the year, then use the fake year with the Text() function to format only the month and day, and finally append the real year.

If you need to perform other actions with these dates, you may need to come up with similarly creative solutions.

Access can store all dates as far back to the year A.D. 100.  So if you have tons of these old dates, consider using Access to store them.  Sadly, even if you import Access data into Excel, Excel still won't show these dates correctly.

I made a blunder: Sunday is for the date 7/4/2776, not 7/4/1776.  7/4/1776 was actually a Thursday.  We would have to use Access (perhaps with VBA automation) to find the correct day.

Good catch. Yeah, I've never used Excel for anything other than "modern, current" dates. Here's my take on how to handle crazy old or far in the future dates in Access: How to Handle BCE Dates