Thank you for your question and the very detailed story you shared here.
If I'm understanding you correctly, you are living and working in Israel and your ex-girlfriend is in Germany (and from there) with your baby, is that correct?
I can understand why your situation stresses you and can imagine that it must be hard being apart from your baby.
1. To answer your question whether or not you can go to Germany: as a Colombian-passport holder, you are allowed to enter Germany visa-free, according to a Germany Visa Website: "According to Germany short-stay entry rules, the residents of 62 third-world countries are permitted to enter Germany visa-free and remain there for a period of 90 days within 6 months. During this period, visitors are not permitted to work, but they can engage in business."
2. Regarding the paternity acknowledgement/ Vaterschaftsanerkennung: from what I could find during my research, acknowledging paternity is a voluntary act to be the father of the child bound by law. However, if a father denies to acknowledge paternity, a court case may be introduced / a DNA-test may be made in order to determine who the legal father is.
If a woman determines a man as the (legal) father, no test will be made. It is "irrelevant" if he is the biological father.
Please check this website for more legal information on paternity. The source is in German, but you can try a translation tool: https://www.anwalt.org/vaterschaftsanerkennung/#Rechte_und_Pflichten_nach_einer_Vaterschaftsanerkennung
3. In any case: it would probably be best to find a solution with the mother - maybe you can kindly ask her again to talk about your rights to see your child and that you would not want to miss out on its life. As you two aren't married, she has sole custody of your child and can decide whether or not she will share custody with you (or how often you may see it, etc.).
I hope this information helps. Feel free to reach out to us again or browse on our platform for more information on child custody and paternity acknowledgement. Simply use our search bar on the top right!
All the best,