Your word choice leads me to want to answer to separate but overlapping questions: did becoming a father make me a better PERSON? and did becoming a father make me a better MAN?
As a man that is now divorced and came upon fatherhood without planning to do so, I may have a perspective that is uniquely appreciated or may be particularly disdained, but I will offer my thoughts nonetheless.
As a MAN: I immediately became a better man, defined as I became immediately better at fulfilling roles/duties that are historically/stereotypically defined as masculine. Mainly, I learned how to fix things, I started working more (and thus earning more money for the household), and I became the source of discipline and even became very strict (previously I would have thought that I would be a more liberal, hippie of a dad, but while I am a pinko at the ballot box, I am the metaphorical Ronald Regan at home).
As a PERSON: I immediately became a better person as well. I started trying to take better care of my health, I became faithful as a partner, and I became more respectful to my own parents.
BUT, these things were immediate changes for the better, but they all came at a hefty price. When you have a child, you HAVE to change, you are forced to work and you are forced to discipline and you are forced to do many things. The stress of being forced into those roles caused me great personal drama and pain because I was not ready for those things and irresponsibly created a child I was not ready for. That nearly destroyed me as a person and as our home. As someone that is still in reproductive age, I am never going to have a child that I am not 100% eager and ready for, and would counsel you not to so either. The things I identified above were positive changes brought about by my child, BUT they were things that I SHOULD have changed or been BEFORE having a child. I think you are only really ready for fatherhood or parenthood when you are 100% self-fulfilled already, after all that kid is looking to you to have the answers and if you don't you just failed in your job.
So in summary, yes being a father made me a better man and person because I had to rapidly try to become a good person/responsible person/ wise person, but that was the backward role, you should only have a child when you already are a great person/responsible person/ wise person. I other words, as a father your duty and job is to have life figured out so that you can explain it to your kid. If you don't have life figured out and are hoping that child-rearing will help you figure it out, use protection.