Details

Handling dates as string is easy, but we still need that DateTime

Use this static DateHelper method to convert string to DateTime

public static DateTime? ParseDate(string input)
{
   // Define common date formats
   var dateFormats = new[]
   {
       "MM/dd/yyyy",
       "dd-MM-yyyy",
       "yyyy-MM-dd",
       "MM.dd.yyyy",
       "yyyy.MM.dd",
       "dd/MM/yyyy"
   };
   // Try parsing with any of the specified formats
   if (DateTime.TryParseExact(input,
                              dateFormats,
                              CultureInfo.InvariantCulture,
                              DateTimeStyles.None,
                              out DateTime parsedDate))
   {
       return parsedDate;
   }
   // Return null if parsing failed
   return null;
}

Don't forget to cast the parsed date to DateTime

var parsedDate = DateHelper.ParseDate(input);
// Perform check…
user.DateOfBirth = (DateTime)parsedDate;

Unless what you need is a nullable DateTime?.