It is in fact the belief of the reformers, essentially calvinism.
Regeneration comes first is what they believed.
https://carm.org/does-regeneration-precede-faith
I used to believe the other way, but found it not scriptural.
We are saved by His mercy, hence total grace and love poured out onto us.
He did this by regenerating us, renewing us in the Holy Spirit.
As you can read, no mention of belief at all here!
Just poof, you will be saved. Which is the being born again part, afterwards when you believe you are sealed. All those regenerated are essentially saved, but have not made the good confession yet, but they WILL, people believe from the heart, the heart is what gets regenerated, so you can see what comes first..
Titus 3:4-6 English Standard Version (ESV)
4 But when the goodness and loving kindness of God our Savior appeared, 5 he saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit, 6 whom he poured out on us richly through Jesus Christ our Savior,
Romans 10, does not disagree with regeneration precedes faith.
9 because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved.
10 For with the heart one believes and is justified, and with the mouth one confesses and is saved.