OP - it's very likely it's his child - single parents don't find it easy to date much, so what are the chances.
Don't try to give this a go. You would feel sick every time the phone rings, for a good year or two.
Every other weekend isn't very much - but your partner will put all his overtime work and life admin into the other weekend, and you will notice that for you, the 'good' weekend is the childfree one, while for him it is the one with the child. So there will never be a good weekend. You will find the weekends with the child tiring and full-on, when you had planned for other priorities, perhaps adventures, over the next few years.
There may be some game-playing and tension until they work out a good co-parenting relationship. He will share some of the drama with you and you will be angry and upset. However, you will also find it hard to cope with the joy and all the upsides - because it isn't your own child.
When you come to buy a house you will need to pay for an extra bedroom. He might well decide he can only afford to have two children - while perhaps you would like two of your own. And this might be years into a marriage where he initially signed up to what you wanted - but he can always reasonably choose to prioritise the needs of his current child, and change his mind.
There will be nursery fees, and later on, extortionate school trips that you would never agree to for your own child, that your partner feels pressured to fund. There are college fees and living expenses, perhaps well into their 20s. Also support for a deposit on a property, a first car and first wedding. You will feel guilty for feeling resentful, but also feel that it's a high financial price to pay, and that these are things you weren't raised to expect, and didn't expect to provide for your own children.
You will be asked to do pick-ups when he is unexpectedly working late, or if the child's mother is unwell. You will find that your job becomes less important to him - for example, if you have a big deadline but you're needed at home. You will find yourself taking on a lot of responsibility that you never expected. If you have your own child, you will find that you are carrying more than half of the load for your own child - and you might suspect he finds his other childcare commitments quite convenient at times. You and any children you will have will have to work around the pickups and school runs and first child's activities and social life, and you will begin to mind on behalf of your own child that your partner just cannot do as much. And the child themselves may not warm to you, and may have challenges and needs that would strain even the strongest relationships.
And if you ever voice resentment, people will shut you off because they always put themselves in the shoes of the mother rather than the new partner. Because most people would not take this on - they recognise they would not be up to it. So, since they rule it out as an option for them, they assume that if you have kept it as an option for you, you must have known what you were letting yourself in for, or perhaps that you were unlikely to meet anyone else and you should just be grateful. They may also assume the relationship was more serious than it was, or that he was not honest with you, or perhaps that you were the other woman.
There is a lot of social pressure on women to accept male mistakes because the bigger picture is the needs of the child - and of course the needs of the very important male partner. Women are expected to be helpful and forgiving. But you only get one life, and you're young. Too much of his time, attention and finances will be elsewhere rather than the joint future you had in mind. It will demoralise you bit by bit.
The saddest thing will be if he truly is as lovely as you say. He will feel guilty and he will be so, so sorry. Even if you decide to carry on, it's quite likely that you would then cope by building more of a life of your own. Which he would struggle with, because he wanted the dream, a lovely family life and children with someone he truly loves, and will react to you being more detached. You may then find yourself having to comfort him as he processes how his life has changed in ways he didn't expect. You will find that you are always the third priority.
Or, you could meet someone else, and have a better chance of everything you dreamed of. Perhaps talk to a counsellor who can help you work out what it is you really want, and whether he really is a non-negotiable part of your future.