i think it needs to be said that as kids grow up, dad's circumstances might change - and all of a sudden he decides he wants access/shared care etc. and they can make life difficult if they show up when your child is a bit older

i would do all you can to prove paternity now - if he decides to be a deadbeat, so be it - at least your child won't hold it against you that you KNEW who their dad was and didn't do what you could to establish a relationship. it is definitely better for you and your relationship with your kidlet (long term) for them to know you tried. the last thing you want to do is to know that the dad is a deadbeat that doesn't want access but not have the proof (CSA/court docs) to prove it to a teen child who's "good time" dad has just arrived on the scene sprouting crap about you... i've seen it happen to a friend (similar circs to you) whose DD is 15-ish and her "dad" just appeared on the scene saying that the mother was lying about him, he never knew about her blah blah blah - not pretty