As a consequence of Adam's transgression, he died spiritually. God had said, "in the day that thou eatest thereof thou shalt surely die (Gen. 2:17). That is why Adam tried to cover his nakedness and to hide from God (Gen. 3:7-8). Because all of mankind bears the likeness of Adam (Gen. 5:3; 1 Cor. 15:22), we all sin (Rom. 5:12); we are all said to be (spiritually) dead in our trespasses and sins (Eph. 2:1). That is why Jesus taught that a man must be "born again" spiritually (Jn. 3:3-8; 1 Pet. 1:18-23).
After Adam sinned, he still had access to the Tree of Life. "So He drove out the man; and He placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life" (Gen. 3:24). Had God not forced Adam and Eve to leave, they could have lived (physically) forever. They would not have feared their physical death, followed by their certain judgment before God (Heb. 9:27). So He blocked "the way."
Have you ever heard the saying, "When God closes one door, He always opens another?" Well, that is exactly what He did. Not willing that any should perish (2 Pet. 3:9), before He closed "the way" to the Tree of Life, He had already opened "The Way" to eternal life (Jn. 14:6). God was prepared for Adam's transgression; we see this from several Scriptures (Mt. 13:35; 25:34; Eph. 1:4; 4:3; 1 Pet. 1:20; Rev. 13:8; 17:8). God willed that all should be saved, and He provided "The Way" for that to happen. It is up to each of us to accept God's "Way": Jesus!
"Believe on the Lord Jesus Christ, and thou shalt be saved" (Acts 16:31)!