The Spirit Jesus says gives life, that's when Faith is given, for its a Spiritual fruit Gal 5:22
When one believes
Gal 5:22 is not speaking of initial saving faith
It is vicious hermeneutic you employ which seeks to interpret the bible in contradiction to itself
without faith one cannot receive the spirit
John 7:38-39 (ESV)
38 Whoever believes in me, as the Scripture has said, ‘Out of his heart will flow rivers of living water.’”
39 Now this he said about the Spirit, whom those who believed in him were to receive, for as yet the Spirit had not been given, because Jesus was not yet glorified.
Galatians 3:2 (ESV)
2 Let me ask you only this: Did you receive the Spirit by works of the law or by hearing with faith?
Galatians 3:5 (ESV)
5 Does he who supplies the Spirit to you and works miracles among you do so by works of the law, or by hearing with faith—
Galatians 3:14 (ESV)
14 so that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we might receive the promised Spirit through faith.
and according to the bible life which the spirit supplies follows faith
John 20:31 (ESV)
31 but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name.
John 5:24 (ESV)
24 Truly, truly, I say to you, whoever hears my word and believes him who sent me has eternal life. He does not come into judgment, but has passed from death to life.
John 5:25 (ESV)
25 “Truly, truly, I say to you, an hour is coming, and is now here, when the dead will hear the voice of the Son of God, and those who hear will live.
John 5:40 (ESV)
40 yet you refuse to come to me that you may have life.
you still got it backwards