I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today.
Under CO law, as your ex is not named as the father on the birth certificate, and there is no record of him being the natural father, he has absolutely no legal right to custody or visitation of your child and you are under no legal obligation to grant him visitation.
In order for him to even have visitation rights, he would have to apply to the court for those rights and you could use his sexually violent history and outstanding warrants for arrest as a legal basis to deny him visitation.
There is little reason to be concerned about his filing for visitation in the near future as that would open him up to arrest on the warrants and you can use his sexual offender history to seek to prevent visitation.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
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I wish you and yours the best this holiday season,