From the search field you can search for parts of a date, for example the month or a year, but not a specific date.
For example, the search for "March 2018" will turn up a search result "Date, Date", if you have photos within this date range.
As to smart albums - I second Keith's recommendation to use smart albums for searching. I am keeping one smart album just for searches.
In Photos 4.0 on Mojave are two different date searches - "date captured" and "date added". Be careful to pick the right smart rule to search for the date the photo has been taken and not the date of import.
Is your Mac set to use English as the system language or are you using another primary system language? On earlier systems Photos used to crash when using a date rule, if the primary language has not been English. I am not sure, if the problem still persists.