Hebrews 1:10-12 is our authority for regarding Psalm 102 as Messianic:
These words, addressed to God's beloved Son, are a quotation from the 102nd Psalm (vv. 25-27).
The title of the psalm, however, "A Prayer of the afflicted, when he is overwhelmed, and poureth out his complaint before the LORD," and the first twenty-four verses are in complete contrast to the last stanza. In the title and the first part of the psalm we see the Lonely Man of Sorrows, but in the latter part the Immutable, Unchanging, Eternal God!
These, then , are the two parts of the psalm:
Aren’t you glad that God is not like men, who change from day to day, if not from moment to moment?