Paul Ekman had this “theory of basic emotions” that were supposedly universal for humans and had their set of “innate” gestures for each one.
For his original works, he travelled to some secluded communities and registered that the expressions for “happiness / fear / anger / disgust / sadness / surprise” were supposedly shared among human kind.
Why do I say supposedly? Because a lot of Ekman’s theory was disproved (for example, he claimed each emotion had an area of the brain dedicated to it, or at least some unique structure, which fMRI studies are not finding to be true, even if there is a lot we still don’t know on human emotion). There’s also claims that he contamined his data when he went to these secluded communities, and influenced (probably unknowingly) his results to make everyone’s expressions match the ones he expected for each emotion.

So… are there universal expresions of emotion? Not an easy answer. The physical responses more linked to survival probably are (say fight/ flight in response to fear, startle in response to surprise). The more social ones? don’t know, some may be heavily influenced by culture. You would have to make a study on very young, blind babies from different cultures or something of the sort which would not be easy. Also there’s the thing that babies cannot tell you what emotion they are experimenting, even if you can asume some (loud noise and baby is crying probably equals fear, BUT the baby can’t confirm it, which is a methodological problem for some Scientists).

If this interests you, Ledoux has some great approachable work on the “survival circuits” of the brain that explain emotion in a way comparable to animals and linked to their evolutional value.

Paul Ekman demonstrated back in the 1960s that, when showing photos of expressions to previously-uncontacted tribes in Papua New Guinea, these people who had no access to other media recognised and could name the feelings described. Also, blind children who have not been told what “a smile” is, will display the facial expression automatically. This research finding was one of the nails in the coffin of the Behaviourist school of psychology (with rats pulling levers) that said everything was learned by rewards/punishments.

Ekman identified 6 “basic” emotions: happy, sad, disgusted, angry, scared, and surprised (which, except for the last one, were the characters in Pixar’s “Inside Out”). Later researchers have proposed a seventh emotion of “pride”, which has the posture of puffed-out chest and smug half-smile, which again is displayed by blind athletes on winning competitions.

I remember reading that, during the Vietnam war, there were many issues when American soldiers would confront Vietnamese soldiers or citizens who would be smiling during the confrontation. The American soldiers took it as a sign that the Vietnamese were screwing with them somehow. It turned out that, for the Vietnamese, a nervous smile was very common.

Among humans, many seem to be somewhat universal. Across species, no - non-human primates (apes and monkeys), for example, may consider a smile a sign of aggression.

some of them are present in the mammal world, so I’d guess they are universal among humans, at least to a certain degree