It is not so much that the Father is drawing people who don't know God to Jesus; he is drawing those who know him to meet his Son.That is, the passage is not so much about drawing men to faith in Jesus from a position of non faith, but drawing men who already belong to the Father so that they may also trust Jesus.
Others have commented that the passage
Jesus answered them, “Do not grumble among yourselves. No one can come to me unless the Father who sent me draws him. And I will raise him up on the last day. (John 6:43–44)means that the Father is drawing people to faith Jesus. That is to become a Christian from a position of unbelief one needs the Father to draw him.
Now I think that the passage as it stands alone could say that. Further, regardless of this passage I believe God is wooing men that they may come to him.
However, the larger context of John 6 causes me to question the common interpretation. As I show in my earlier post, Jesus is repeatedly associating himself with the Father and connecting his mission with the Father's mission. The point of the passage is to make this connection. The Father is in the Son and the Son is in the Father, compare John 10:30. 1 John 2:23 says.
No one who denies the Son has the Father. Whoever confesses the Son has the Father also.John throughout his gospel and his letters identifies the Son with the Father. Although one could read the passage about the Father drawing in isolation to mean that God draws unbelievers to salvation in Christ, it is more in keeping with John's message here and elsewhere to read the passage as God drawing his own to Christ: the Father revealing Jesus.
Confirmation of this interpretation is seen in Jesus calling himself the manna from God. "It was not Moses who gave you the bread from heaven [God did], but my Father gives you the true bread from heaven." Jesus is saying, "God is giving people me. God is drawing men to me." It is not about drawing men resistibly or irresistibly, it is about giving men Jesus.