In essence, this is where logic begins to fail us. That is also why the other religions that are not based on revelation do not teach that their gods are personal, because human knowledge alone cannot determine that. We know God is personal because God told us, and He proved it to us in history.
The best way for us to demonstrate it is through Jesus’ Gospel and our own personal story with God. Jesus’ Gospel story is a historical story, and it is compelling. In honesty, one either has to dismiss if Jesus ever existed, or has to take in the whole Jesus as it is presented; anything in between is in one way or another a form of intellectual dishonesty. And Jesus’ story is a testimony of a personal God who is our Father, in love with us and seeking to embrace us to Himself.
And then there is your own story. If you have encountered God, You cannot but radiate God’s love, peace and joy in your life, because God has made a difference in your life and has set you on a different course. Those who are truly walking with the Lord live a life that others often notice to be inexplicable if God does not exist.