Some of the sacrifices, namely, those that have a fixed time, can be offered despite there being contact with the dead, Tumat Meit, if the majority of the community is also impure, due to Tumat Meit.
While there are some limitations to this halacha, that I don't want to discuss right now, perhaps, the Rabbis will agree on some method to make use of this halacha, to restore sacrifices immediately.
Also some Rishonim claim based on the Talmud, that ashes of the red heifer, Para Aduma, still existed from what was produced in Temple Times, hundreds of years after the Temple was destroyed.
Perhaps, one day we can rediscover those ashes.
I read in a book Geula Bederech Hateva, by the historian, Morgenstern, that at least one of the major disciples of the Vilna Gaon, claimed {if he can be believed} that he knew where such ashes were located if ever they would be needed.