Question is pretty self-explanatory. Either way, a date on a calendar is a date. When it becomes unexpected, it sounds right to me to say an unexpected date instead of a unexpected date. Same for when using expected.
Which one is it?
“a” is used when the next word begins with a consonant sound
“an” is used when the next word begins with a vowel sound
Therefore it is “an expected completion date” (also I would pronounce the “an” more nasally so it is not confused with unexpected)