Some universals are certainly shared with other creatures, and it's not even restricted to mammals. From one article: Take, for example, social facilitation or

Some universals are certainly shared with other creatures, and it's not even restricted to mammals. From one article: Take, for example, social facilitation or the notion that organisms tend to perform better on simple tasks in the presence of observers. Although disagreement about its innate origins exists (Do-Yeong and Junsu 2010), social facilitation has had supportive evidence in humans in a natural setting (Michaels et al. 1982), cockroaches (Zajonc et al. 1969), and macaques (Dindo et al. 2009). (I don't know about facial expressions, though the fact that I don't know means little - I've just read a bit about it.) There are other universals among non-human species, not shared with us, such as 100+ discovered for chimpanzees. Source: Reza Ziai, "Cross-Cultural Universality". In Todd K Shackelford, Viviana A Weekes-Shackelford, eds. Encyclopedia of Evolutionary Psychological Science. Springer (2021)