For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast. (Ephesians 2:8-9)
In Ephesians 2:8-9 Paul is making a contrast. There is something from God. It is a gift as opposed to something we work for. The gift is not faith because then the contrast wouldn't make sense. Whoever heard of working for faith? The gift is salvation, not faith.
"...the gift of God is eternal life through Jesus Christ our Lord." (Romans 6:23)
By His grace God gives salvation. By faith we receive His gift of salvation. God offers it to all, but only those who by faith receive it are saved.
"For this is good and acceptable in the sight of God our Saviour; Who will have all men to be saved, and to come unto the knowledge of the truth." (1 Timothy 2:3-4)
"For therefore we both labour and suffer reproach, because we trust in the living God, who is the Saviour of all men, specially of those that believe." (1 Timothy 4:10)