The scriptures are clear that man has the ability to choose whether he yields himself to sin, or righteousness.
Rom 6:16 Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?
17 But God be thanked, that ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you.
18 Being then made free from sin, ye became the servants of righteousness.
Romans 6:16 shows man has option and choice. Whoever he yields himself to, he becomes servant, "whether" (option) of sin to death, "or" (option) of obedience to righteousness.
That the sinner has the ability to obey the gospel is clearly stated in verses 17 and 18. Paul says God be thanked that "ye were" the servants of sin, but they have obeyed from the heart the doctrine delivered them, that is, believed the gospel.
It was THEN, after believing the gospel that these sinners were made free from sin, and passed from death to life.
So, scripture is perfectly clear that sinners have the option and ability to believe the gospel and when they do they become servants of righteousness.
Regeneration before faith is utterly ridiculous and logically impossible, because until you believe you are dead in trespasses and sins.
Regeneration does not mean to be illuminated, or enlightened, or made aware, it literally means to be made alive again, to pass from death to life, which only happens after one believes.
Jhn 5:24 Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life.
John 5:24 clearly shows faith precedes regeneration.