Viruses do it all the time. It can indeed cause trouble, but a random mutated rhinovirus is more likely to do so (allergies, typically) than a vaccine which was developed specifically to not cause any damage.
This idea that "We are not gods." Such a peculiar argument. If something is capable by a mortal man what makes you think it has god-like qualities? To me it is the opposite. Also since you're using the word "gods" are you referring to polytheism? Where did you decide you were capable of determining a "god-like" thing? You. Are. Confusing. Me.