We don’t need Mashiach to come in order to bring a korbon Pesach.
There are records of R’ Yechiel m’Paris, who traveled to Eretz Yisrael to try and bring a korbon Pesach. However, he couldn’t determine the exact location of the mizbeach, so it didn’t happen.
Later, R’ Akiva Eiger asked his son-in-law, the Chasam Sofer, if he could convince the Sultan to allow Jews to go on the Har haBayis to bring a korbon Pesach. The Chasam Sofer replied that the Sultan would never allow Jews to bring any sacrifices on the Har haBayis, so it couldn’t happen. However, the Chasam Sofer clearly wrote that we are allowed to bring a korbon Pesach from a halachic perspective.
