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actually, most calvinist would hold that BOTH happen at the same moment from our point of view, as the Lord grants the new heart on hisside, and we place faith in Jesus 2 sides of the same coin!
Those such as Strong and Spurgeon held to same time, usually extreme Hyper cals hold to regeneration proceeding faith to a large time differential!
It doesn't matter if you believe they happen at the same time, the scriptures say you do not receive the Spirit until you first believe. In fact, many in the NT did not receive the Spirit until days after they believed.
Acts 19:1 And it came to pass, that, while Apollos was at Corinth, Paul having passed through the upper coasts came to Ephesus: and finding certain disciples,
2 He said unto them, Have ye received the Holy Ghost
since ye believed? And they said unto him, We have not so much as heard whether there be any Holy Ghost.
3 And he said unto them, Unto what then were ye baptized? And they said, Unto John's baptism.
4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
5 When they heard this, they were baptized in the name of the Lord Jesus.
6 And when Paul had laid his hands upon them, the Holy Ghost came on them; and they spake with tongues, and prophesied.
Paul's question in verse 2 shows that he believed a person receives the Holy Spirit AFTER (since) they believed. And in fact we see these disciples did not receive the Spirit until after they had believed on Jesus and been baptized in his name.
But you are correct, some here believe a person can be regenerated for a long time, possibly years before they actually believe on Jesus. Luke recently said he believes a person can be regenerated for a LONG TIME before he is saved. He didn't explain how long this time was or what he meant by being saved.
Until you believe on Jesus you are DEAD IN SINS. You cannot possibly be spiritually alive until AFTER you believe.
Eph 1:13 In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also
after that ye believed, ye were sealed with that holy Spirit of promise,
You can believe whatever you want, but the scriptures say a man receives the Spirit AFTER he believes, not at the same time.