R’ Herschel Schachter has a fascinating piece on this idea.
He writes that the definition of galus is the deprivation of gilui Shechina. The full gilui didn’t come until Matan Torah, so the geulah wasn’t complete until then. There were stages to it, it began with Pesach, but didn’t end until we had the Shechinah.
He notes that we’re told that we are destined to be redeemed in Nissan, but we also say b’chol yom sheyavo – Mashiach can come any day. The contradiction is answered that the 3rd Beis HaMikdash won’t be dedicated until Nissan. So while Mashiach can come at any time, our redemption won’t be complete until we have the gilui Shechinah, with the new Beis haMikdash, in Nissan.