The gospel is the power of God unto salvation. It doesn't say it is the power of God for being born again. All that is required to be born again is the Spirit. He makes us spiritually alive.
ROFL You think being born requires no power? I gave birth to three kids, took all my energy, especially the first. In fact I was so exhausted I couldn't even hold her in my arms. I had to call the nurse over before I dropped her.
My argument has not been what you are trying to make it now. Stop moving the goal posts.
Being born requires power on behalf of the one birthing which, in the case of regeneration, is the Spirit. You received that power and you said only believers receive God's power. So either you believed before regeneration or you did not and received power as an unbeliever. We are talking about power to be born, not the power of the Gospel unto salvation.