That is not what that verse is saying.
Look at the entire chapter. Paul is telling Titus what lifestyle will allow the grace of God to “shine forth” or appear to all men. The Greek word used there is epiphainó which means I appear or shine upon. It certainly does not mean that God gave that grace or faith to unbelievers.
"hath been made to appear," or "shine forth" (Isa 9:2; Lu 1:79). "hath been manifested"
For the saving grace of God was manifested to all men.
John 1: 8 He was not that Light, but was sent to bear witness of that Light. 9 That was the true Light, which lighteth every man that cometh into the world.