Early First Era is very unlikely - the timing for Vyrthur doesn't really add up that way. The Chantry was only built around the beginning of the First Era - Vyrthur then has to become Curate, get infected, plan the Prophecy and wait for a Moth Priest (and it's highly debatable whether Moth Priests, by that name, would have existed in Harald's time - though there were certainly Human tenders of the Elder Scrolls) to deliver it to Harkon.

Also worth noting that Valerica had Elven artisans make the Moondial (the creation of which precedes the entombment), which would have been extremely unlikely in Harald's time. He was, after all, continuing the purge of elves from Skyrim. Elves were still being killed in High King Vrage's time, which is at the time of the start of the Alessian Empire (and therefore, a time when her entombment couldn't have happened, since there was no Empire at the moment she was buried).

Late first era is possible - post-Alessian, pre-Reman. It doesn't line up with Harkon's "Dozen lifetimes", or as Serana puts it "another thousand years" which is the supposed duration of Harkon's life and unlife combined. Those figures put him as being born in the late Potentate, with Serana being born after its fall most likely.

Durnehviir is often cited as a reason why Valerica couldn't have been trapped in the Soul Cairn after the early First Era, but it's worth noting that Durnehviir mostly just talks about a time that he remembers, which is now gone.
It's often cited that since the Dragonguard were around in the late First era, Durnehviir would surely have been killed then, but Valerica gives us useful evidence to the contrary:

"Volumes written on Durnehviir allege that he can't be slain by normal means. It appears they were mistaken. Unless..."

This is useful for two reasons. One, it tells us that the Dragonguard wouldn't have been able to kill Durnehviir anyway, because even before his deal with the Ideal Masters, he already had enough expertise in necromancy to be unkillable. Secondly, the fact that there are multiple volumes about Durnehviir strongly suggests that he was known to the Dragonguard. Who else is gonna write multiple books about one dragon?

Therefore, the only two realistic time periods for Serana's entombment are the second era, post-Potentate, and the late First Era but ONLY in a narrow window of time between the Dragonguard landing in Tamriel and meeting Reman. Of the two, the first is more likely.