What we call life...is the combination of the Five Aggregates, a combination of physical and mental energies. These are constantly changing; they do not remain the same for two consecutive moments. Every moment they are born and they die. 'When the Aggregates arise, decay and die, O bhikkhu, every moment you are born, decay, and die.' This, even dow during this life time, every moment we are born and die, but we continue. If we can understand that in this life we can continue without a permanent, unchanging substance like Self or Soul, why can't we understand that those forces themselves can continue without a Self or a Soul behind them after the non-functioning of the body?
According to the Buddha's teaching the beginning of the life-stream of living beings is unthinkable. THe believer in the creation of life by God may be astonished at this reply. But if you were to ask him 'What is the beginning of God?' he would answer without hesitation 'God has no beginning', and he is not astonished at his own reply.