I think part of the issue here may revolve around a misconception about faith and what the Bible actually teaches us about faith and God’s salvation for us in Christ.
(1) The Bible does not teach us that faith is a gift to all mankind. Rather, it teaches us that God loves the world and gave His Son to die for our sin (John 3:16). This is God’s gift to the world or all mankind.
(2) Christ is God’s gift to the World. As a result of what Christ did on the cross, salvation or the forgiveness of sins is also a gift that God wants to give to the world, but in order to receive any gift, it must be received (cf. John 4:10; Eph. 2:8-9; Rev. 21:6; 22:17).
The means or channel for receiving Christ is faith—personal trust in Him. John 1:11-12 says, “But as many as received Him, to them He gave the right to become children of God, even to those who believe in His name.” Note that one receives Christ by believing in Him. To believe in Christ means that we believe the witness that God has given regarding the person (He is the God-man Savior) and His death on the cross (He died for all the world and paid the penalty for every persons sin) (see 1 John 5:1 and 11-13). To believe in Christ is to not only accept the fact that there is nothing I can do to save myself, but to trust in the fact that God has promised that when I believe in Christ, my sins are forgiven and He declares me righteous before Him, even though I am still a sinner.