An altar made of unhewn stones is an Adam drawn from the ground, assembled but not yet "filled" with fire (breath) from heaven.
The Temple's "dressed" stones are bridal. The sound of the chisel could not be heard.
One is earthy, one is heavenly. We see the same difference in the Bronze Altar (death - outside the tent) and the Incense Altar (fragrant spices - resurrection).
So an unhewn altar is raw Adam, not yet filled, and not yet "cut" (without hands) to begin construction of the bride.
There are counterfeits to this, grabs for glory before God's time - the "bricks" of Babel and Pharaoh. Babel is always built quickly, using slavery and robbery, but God's cities take longer to build because they are constructed in righteousness.
Another like symbol is the names of the tribes on the High Priest's shoulders. They all look alike - like children. They are Adamic in a sense. But the "fiery" gemstones on the breastplate are the "mature" bridal versions. They are cut stones, filled with fire. Each has its own glory.
So, "uncut" is earthy, outside the tent (like Adam and Cain and Esau) and "cut" is heavenly, or bridal. God's people are cut off from the world, tested, qualified and re-enter the world to serve him. Those who remain "natural" are not cut off from the world, but eventually are cut out of history.
The knife and fire at the Garden gate are sacrificial, transformative. Every man is to be an altar, a miniature Sinai - hence the flames on the heads at Pentecost. Then we see those same altar-men glorified with "Tabernacle metals" for their apostolic witness in Revelation 9. Like the new Israel that took Jericho, the firstfruits saints are mustered to "circumcise" Herodian Jerusalem and put her under the ban. Pentecost makes every man a Tabernacle, a gate, a minister of knife and fire. But it begins with an unhewn stone outside the camp.
The statue in Daniel 2 is a "Gentile tabernacle." At its foot are the Herods (Edomites) as red clay, attempting to "intermarry" (as a harlot) with the statism of Rome (the beast), but, like Cain, without a priestly mediator before God. Jesus came as an altar stone, like the one under Jacob's head at the foot of his "ziggurat," a true foundation for glory.
One more point: the stones picked up to execute the death sentence are the ground itself taking vengeance, gnashing upon flesh with its teeth in a sense. If blood was not avenged or atoned for eventually the Land would vomit the Covenant people out, which Jesus refers to in Revelation 3:16. He is the new Land. We are buried in Him, resurrected and dressed as bridal stones.