Adam and Eve, before the fall, had the Holy Spirit. The Bible doesn't expressly say it, but it explains a lot about how they changed within themselves when they disobeyed God. When they rebelled against God and allied themselves with Satan by following him instead of God, they lost the Holy Spirit, and therefore reverted to their flesh nature which was corrupted by their sin.
This was the amazing thing about the Day of Pentecost. It was the final act to restore believers to where Adam and Eve were - filled with the Holy Spirit and in intimate fellowship with God. (Now, when I say "filled with the Spirit", I mean being controlled by the Spirit, and not some emotional or sensory experience.) This was more than just speaking in tongues. It was a complete restoration of the believers' standing with God.
Conversion to Christ is the restoration of the relationship and fellowship that Adam and Eve had with God before the fall. Paul defines conversion as "having the Holy Spirit" in Galatians 3:2.
So, Adam and Eve had the Holy Spirit, then lost Him through disobedience and siding with Satan. Converted believers regain the Holy Spirit because they side with God against Satan.
That explains how all became sinners because of the rebellion of Adam and Eve. Without the Holy Spirit, sinners are totally in the flesh and have no standing with God. They are totally bound in the works of the flesh as described in Galatians 5. But when a sinner receives Christ, he or she is brought back under the control of the Holy Spirit and lives in the Spirit, with the fruit of the Spirit, and there is a developmental turning away from the works of the flesh toward sanctification and holiness.