If, for whatever reason, you do not do kids at this time, I do not see how you can "give it a go". It sounds like a deal breaker to me when he told you he had kids (does not matter if it was early, late, or whenever).

You have a choice to either work to like kids, be interested in liking kids or to continue to not want to date guys with kids but I don't see this period as being good for you, his child, or him.

Were I you, I would leave before the child comes and come back afterwards if you and he wants, or I would change what you want, to wanting to learn to enjoy the child/children and having him/them in your life.

If you do not like how he handled telling you about his child, that has to be part of your decision but you don't really get a choice of having him without his child unless he were to agree to that. You can have you without his child or you can have him with his child. He obviously wants you. That he made a bid for you with his child; that is his gamble and there's nothing "wrong" with that, we all do what we want for ourselves. You just have to decide what you want for yourself; to learn to enjoy children/this child or not at this time.