Where are you getting this stupid 20,000 year figure from? Even with current tech, we can travel at 0.1c easily, that is without any extra effort made in actually travelling outside our solar system. Near-by candidates are within 20ly, so at min it would take just 200 year, or 3 human generations.

And if it might give you some peace, there are thing called machines that can be built to contact other civilization without sacrificing your hypothetical children.