The angelic Annunciation to the Shepherds of the birth of Messiah in Luke 2:14 contains the phrase "glory to God in the highest". This same Messiah was taken into the "latter house" for His circumcision according to Luke 2:27, performed on the 8th day from birth according to Leviticus 12:3, at which time the name of the child was officially declared and given to the priests for the genealogical record Luke 2:21, a custom still kept by many Jews and some Christian groups today.
I submit that the greater glory prophetically spoken of by YHVH in Haggai 2:9 refers to the moment in time, just eight days after the angels cried out to the shepherds, when Christ was brought into the temple, circumcised, and given His name.
In the somewhat parallel account in Matthew, specifically 1:21, we are told that the reason why the Messiah was named Jesus was because He would save His people from their sins. In such a context, consider the following verses as having some bearing: Psalm 79:9, Isaiah 46:13, Revelation 15:4 and 19:1.
As the Incarnate Word, Jesus, therefore, as Begotten Son, is the very glory of God. And that glory was brought into the "latter house" mentioned by YHVH in Haggai 2:9.