It's all symbolic. The cross shows the nexus of all time as all things are brought together in Him. He was slain before the foundation of the world and so every moment that came before is looking forward to that time and everything that came after is looking back. Really, that is the foundation and everything is laid on it.
This was prophesied in the constellation the southern cross which was visible in the holy land in ancient times; but is now only visible in the southern hemisphere. This is probably why some ancient cultures revered the symbol of the cross and put it on necklaces.
He's lifted up from the earth. Suspended in between heaven and earth showing He is the link between the two. He's put on a tree to show He takes the curses of the Law on Himself to put them to death in His body.
He was lifted up like the bronze serpent; because the serpent represented sin; and if we believe then we see our own sin upon the cross. So if we admit Jesus died for us then we confess we are sinners; because we admit our sins put Him there. Just as they confessed in the wilderness by looking on the bronze serpent and so were healed from the venom.
He was the carpenter's Son and died on a wooden cross. Perhaps made by a carpenter. Anyway, Noah was also a carpenter and God saved them by a wooden boat. This idea may go all the way back to the tree of knowledge of good and evil. By a tree mankind sinned and God said cursed is everyone hanging on a tree and by a tree Jesus brought salvation.