When Mashiah Comes, The Parah Aduma is Not Needed At First
Rav Mordechai Eliyahu ZT"L explained in a shiur how the logistics of purifying everyone when Mashiah comes is solved. See the last paragraph here.
Translation taken from R' Yaakov Nathan's comments on this old post:
Regarding what we said about the red heifer, [about] the third, the seventh [days of purification]:
Moshiach will come now -- where will the third [day] come from, where will the seventh [day] come from? [In other words, purification via the process of the red heifer requires seven full days to pass, as well as a process of sprinkling the water mixed with ashes over each and every individual Jew--a very lengthy process to purify the entire Jewish people.] What are we going to do now, we won't be able to touch Moshiach? We won't be able to touch Eliyahu Hanovi? Imagine when my turn arrives...[The Talmudic sages] Abaye, Rava, Ravina, Rav Ashi will all be alive [and in need of purification]...until my turn arrives [as I will have to wait behind all the great sages of previous generations] it will be a long time.
[Therefore, to solve this logistical problem] the Holy One says, "I will make a temporary law for you." The Torah belongs to G-d, the laws are his [so He can make a temporary law if He desires]. He makes a one-time law: "I will pour upon you pure water and you will be purified" (Ezekiel). The heavens will open up...
It is written that when Hashem created the world, the water was split--half was placed above, half was placed below....When Moshiach will come Hashem will open up the heavens and "I will pour upon you pure water and you will be purified". We won't need third, the seventh [days], we won't need the ezov, we won't need the red heifer...the Holy One says "One time I will permit you [full purification without the seven day waiting and sprinkling process]. Afterwards if you become impure you'll need the red heifer, but now I will make it easy for you: "I will pour upon you pure water and you will be purified" and it should be Hashem's will that it happen very speedily in our time, Amen!