What means the sealing, the earnest, and our hearts? Perhaps we can see God's dream in this.
When you read the verse 2 Cor 1: 21b "and hath anointed us, is God;
22* Who hath also sealed us, and given the earnest of the Spirit in our hearts."
I am deeply touched that God, himself, has sealed us unto himself as a done deal.
Whatever is given as the earnest is given as a sign of serious intent, and God has given us himself as the earnest in the form of the Holy Spirit. So we know that God has given himself in the form of Christ Jesus to die and be risen for our sins, and God has given himself in the form of the Holy Spirit for our continued guidance, and is serious in his intent.
Further, we read in the Old Testament
Jer 31:33* But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people.
—we could say that God began by writing his law in our hearts, but with the sacrifice of our Christ, he has fulfilled and covered the law in our hearts with the grace of the Holy Spirit. In a sense, he has replaced our lawful hearts of stone with a grace-filled heart of flesh.
We also might ask, "What is God's so very serious intent that he would give himself for our sins and give himself into our hearts as his earnest?" and we find the answer in the Jeremiah passage where he says he shall be our God, and we shall be his people—this is the deal that God has actually done.
To answer the question, in God's own heart, I believe God's "dream" is that he desires to have us as his people and for us to embrace him intimately as our God in glory. The Spirit in our hearts bears witness to this, that we are already one with our Maker through Christ Jesus our Lord.
I know I'm not a Biblical scholar. Please feel invited to nudge me if you feel I'm off track.