Eternal life does not start when your current physical body dies. We are unable to experience eternal life completely in the mortal bodies we currently possess. This because eternal life is forever and our mortal bodies only have a finite existence. But Jesus and his followers demonstrated that we can experience some of eternal life in our mortal bodies.
We can experience eternal life now by surrendering to God. Surrendering to God is a lifestyle. It includes believing there is one God who determines how the Universe works. It includes believing you like to do things God does not like and he will severely punish you because you do them even if you are a good person. It includes believing God allowed his son, Jesus, to be executed so that you can escape God's punishment. It includes believing God loves you and everyone else although there is evil in the world. It includes willing to do what God's want you to do even if it seems difficult, impossible, irrational and causes you discomfort because you know God will give you peace, joy, and comfort by doing so.
Surrendering to God is choosing to obey God because you know he loves you and only wants good things for you although you live in an evil world and you do wrong sometimes.