“Regeneration always preceeds faith.”
No. Regeneration, by definition, means being reborn. It is when we receive life - and that is something that happens WHEN we believe. It is NOT something that makes belief possible.
“But to all who did receive him, who believed in his name, he gave the right to become children of God...”
Those who believe BECOME. They do not BECOME children of God that they might believe. “...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.”
“14And as Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up, 15that whoever believes in him may have eternal life.”
“God always makes the first move.”
True. On THAT, we totally agree.
And yet doesn't Eph 2:8 say "For by grace you have been saved through faith; and that not of yourselves, it is the gift of God"?
According to this Scripture even belief is a gift.