This is going to take time and months to fully play out. I in no way want to come off as flippant or not realizing the magnitude. It is only for the sake of your time that I will be matter-of-fact and leave out the emotional turmoil and long history of my sin.
I'm in my thirties and contacted a female much younger than me off of a hookup app. I engaged in sexually abhorrent things via webchat. I met the female at a hotel in her hometown hours away. I engaged in debauchery and unprotected sex -- alcohol was involved. Sometime later she informed me she is pregnant. I knew her for all of eight hours of my life. She thinks it is her boyfriend's but the date span and something inside me tells me it's mine.
She does not know my real name, phone number, address, or anything. But I read I Timothy 5 and what it is to be worse than an infidel. She and her ex initially were going to abort and she is in no way stable enough to be a mother -- economically, emotionally, or spiritually. I could disappear but Jeffrey, as God is my witness, I do not want to be damned or abandon a child I may be the father of. What do I do? My actions are so grotesque and border on child abuse. God forgive me.
I thought about your note over lunch. I can't figure out your motivations. That you were using an app to find a sexual partner tells me that you've been doing this for a while -- being involved in pornography and fornication. That she contacted you after the fact through this app also tells me that you are continuing to use it. That you were drunk also tells me that you have an alcohol problem and that this wasn't the first time you've been intoxicated. But you wrote to a preacher and know a passage most people don't take note of, so it tells me that you think of yourself as religious. I've seen this many times -- people lying to themselves that they can be worldly and a Christian at the same time.
But what puzzles me is that you aren't focused on your sins. It appears that it didn't really bother you until you found out you might have gotten her pregnant. You are concerned about your future responsibilities and how those might impact your entrance into heaven. Not that being concerned about them is wrong, it just strikes me as an odd combination. Ask yourself: If you had never heard from this girl after that night, would you be writing me in remorse? I suspect the honest answer is "no," and that should be very disturbing.
Let's start out with something you likely already know: "Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived. Neither fornicators, nor idolaters, nor adulterers, nor homosexuals, nor sodomites, nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners will inherit the kingdom of God" (I Corinthians 6:9-10). The statement "Do not be deceived" is important here. You, like too many others, have been lying to yourself that you can sin and somehow God will still let you in. If you want salvation, and I do want you to be saved, then you have to make some really drastic changes in your life because right now you are going in the wrong direction.
I know little about this girl. I can conclude that she's had sex with her boyfriend and other men. What I can't directly determine is why she wanted to have sex with a much older guy. There was something she thought she was gaining, but I don't know what. If she thought the baby was her boyfriend's why would she tell the guy she had sex with one night?
Sadly, I know some people who use the claim of pregnancy to manipulate people into giving money or entering into a marriage, etc. I can't rule out that possibility. You are responsible for your sinful actions, but I want you to first insist on a DNA test before you send her any money or sign your name on a future birth certificate. You don't know how many guys she has been having sex with.
For that same reason, you need to see your local doctor and get checked for STDs.
If this does turn out to be your child, then you will make arrangements to support the child. The arrangement needs to be done through the state's Health and Human Services Department and not directly with the mother. It provides a record that you are fulfilling your responsibilities, it keeps the mother from later claiming you never sent any money, and it keeps the mother accountable to someone. If for some reason the mother doesn't want the child or neglects the child, you will be the person they contact to take over raising the child.
Meanwhile, we are back to the original point: You need to radically change to become a righteous man. "For godly sorrow produces repentance leading to salvation, not to be regretted; but the sorrow of the world produces death. For observe this very thing, that you sorrowed in a godly manner: What diligence it produced in you, what clearing of yourselves, what indignation, what fear, what vehement desire, what zeal, what vindication! In all things you proved yourselves to be clear in this matter" (II Corinthians 7:10-11).