It is not uncommon for a trademark applicant to ignore the date of first use in a trademark application. This is because it seems as if it is a small detail to a trademark application.
However, every trademark application has risk. If your trademark specimen does not have a date, then it is entirely possible that your trademark application may come under attack, especially if the date of first use is many years previous to the filing of the trademark application.
The lesson here is to get the best trademark specimen possible for your trademark application and to make sure that you do not wait to file that application. That lag could come in the form of another trademark owner attacking your application in an opposition or cancellation proceeding.