Do I qualify for Italian Citizenship?

My case should be very easy since my father is Italian and apparently just because of that I should have been an Italian Citizen from birth.

However, my problem is that even though my Dad was in my life growing up, mine and my brother's that is, he is nowhere to be found on our birth certificates. He never claimed parental rights on us, and my mom never made him. He still paid for everything regarding us growing up, but officially he is not in our birth certificates. I'm thinking this is going to be a problem in the case that we do start trying to request our citizenship, right?

At some point in time, when we were like 15 and 12yo, I remember there was a paternity test involved, and so I'm willing to bet my mom must still have the results somewhere proving he is our Dad, plus maybe even pictures of him and us growing up?

All in all, I'm a little lost as if this is something we should even try to pursue or not. Of course having his Italian passport would be awesome, but I don't know if we should even bother.

I'll appreciate ANY help and opinions you may have! thank you!