No matter how you display it (i.e., independent of format string), a date in Calc is a specific day X, where X is “number of days since epoch”.
No matter what date acceptance pattern you use, you can’t make Calc recognice a simple number as a date. When you enter 1988, it will always be recognized as number 1988, not as some day in year 1988 (which would be a number around 32000+). When you later tell LibreOffice to show you number 1988 as date, it counts which day was epoch + 1988 days, learns that (with the default epoch) it was 1905-06-10, and shows you the year of it.
For your purposes: why usual numeric format is not OK to store just year numbers?