The most probable explanation for why there are many endemic plants and birds in New Zealand but no native mammals is that "plants and birds would make ocean crossings to the isolated New Zealand islands, mammals could not."
Birds are capable of flying over oceans, and seeds can be dispersed by wind or water, allowing them to reach and establish themselves in isolated areas. In contrast, most mammals do not have the capacity to make such long ocean crossings without land bridges, which New Zealand lacked for millions of years, leading to the absence of native terrestrial mammals.