The Greeks were dualists, holding that soul and body were distinct from each other. They believed the soul was good and immortal, while the body was evil and mortal. During its duration on earth the soul remained entrapped in the body. At death the soul escaped it fleshly prison and was set free. This was the Greek version of salvation.
Some Jews of Jesus’ day, as a result of Hellenization, began to adopt this Greek concept of life after death. But their belief was not based on the Hebrew Bible.
Jews for the most part made no distinction between the soul and body. For them, humans were mortal beings. They had no clear cut doctrine of life after death, but linked eternal life with an eschatological resurrection. Hence, Jews emphasized living on earth now and not going to heaven in the future.
For Jews the kingdom of God was likewise connected to earth. This is how Jesus and the apostles understood the kingdom as well (“The meek shall inherit the earth”). Rather than speaking of going to heaven, they spoke mainly of heaven coming down to earth (Revelation 21-22).
To explore this idea more fully read my book “Heaven on Earth” (Now available online and in bookstores everywhere).