Umm, I'm just going to point out that she's been in that coffin since the time that dragons still existed, hence why Durnehviir is in the Soul Cairn until Valerica dies.
Some dragons survived from the dragon wars, Mirmulnir for example lived in isolation until the 4th Era. Durnehviir made a bargin to guard the soul carin until the death of Valerica which could have happend two thousand years before Valerica hid herself and Serana away. So there is no way to pin down exactly when Durnehvirr made his bargin.
Then if you take into consideration all of the dialogue from Serana, Valerica, and Harkon, and the surprise of the fact that there is a Cyrodiil based Empire, that places the best references of time that Lord Harkon sacrificed his Thousand Innocents and Valerica and Serana did "the dirty" with Molag Bal, deep within the Merethic Era.
I say this because the first Empire was founded two full centuries into the First Era.
Serana isn't surprised the Dwemer are gone, she isn't surprised the Chimer became the Dunmer. So obviously she was awake and active after those events happened. If Serana awake to see the fall of either the first or second Cyrodill based empire she'd naturally be surprised to wake up and find out it was back.
If woke up and were told Great Britian was a super power you'd be surprised to hear it because for you that was history.
When she was born is irrelevant she could have been born in the mythic era but not sealed away until the late second era. If she was awake to see the rise of Tiber Septim she may have assumed a Skyrim based empire was forth coming.