In linguistics, the term "Universal Grammar" is often heard. In contrast, no one ever tried to propose a theory for universal meaning. Specifically, with no universal meaning, how can we understand each other with different languages?
First, you need to understand the position of 'Universal Grammar' in linguistics. It is a particular theory that grew out of very specific concerns - mostly having to do with learnability of syntactic structures. It posits a set of universal innate constraints on the syntax of languages - and is not really a grammar. It is highly controversial and linguists don't generally refer to it to solve problems of comparison unless they work within the theory.
While there is no 'Universal Semantics' that parallels Universal Grammar (in name or in theory structure), concerns with meaning universals go as far back as Plato (in the Western tradition). When Aristotle was outlining his principles of logic, he was in fact thinking of them as semantic universals. In this tradition, many people have dealt with formal logic and logical semantics as if they were in fact describing universal principles.
Cognitive semantics, on the other hand, posits universals in the shared human experience of the world. We all walk upright, have a similar field of vision, interact with objects in our environment, are born to women, grown up in a social setting, have similar internal biologies, etc. These are all reflected in how language is structured both at the level of syntax and meaning.
(Both the formal and cognitive approaches are described by Lakoff in Women, Fire and Dangerous Things).
Some people have sought to go even further and posit universal semantic primes (most notably Anna Wierzbicka).
You are quite wrong that no one has proposed theories of universal meaning! Although it is extremely controversial, people have proposed several such theories.
On the Chomskian side of things many of the semantic categories would be considered to be universals, possibly all of them (though they are not all grammaticalised in each language.) We can understand each other because the semantic categories of FIRST PERSON or PLURAL etc are things we all share.
The Natural Semantic Metalanguage proposes more explicitly that every language is based on a group of around 60 semantic primes: basic components of meaning which are themselves undefinable and yet present in every language. The list is a work in progress, but after over 40 years of work there is a lot of empirical evidence for most in them in many languages.
If you want to explore a school of linguistics which is founded on a semantic basis, and claims that there are indeed universals of meaning, look at Natural Semantic Metalanguage (NSM) theory at a site at Griffith University (Brisbane, Australia)
Here you can find evidence of solid empirical research and a resultant table of semantic primes (or semantic elements) which are thought to be found in most (if not all) languages. A cross sample of English exponents of these proposed semantic elements are: I, YOU, SOMEONE, PEOPLE, THINK, KNOW, WANT, DON'T WANT, FEEL, SEE, HEAR, NOT, CAN, BECAUSE, IF, MAYBE, WORDS, TRUE, SAY, TIME~WHEN, PLACE~WHERE, A LONG TIME, FAR, NOW, HERE. The most recent edition of the table now claims 65 elements and it is thought to be nearly complete. By way of contrast it is important to realise that possibly most of the vocabulary of any language cannot be glossed word for word to any other language. These primary elements provide the key for clear explanation of meanings to accompany translations.
At the above site you will find downloadable pages giving the exponents of these proposed 65 semantic elements in a sample of languages spread across a diverse range of families.
Also the site offers translations of its content in Arabic, Russian and Chinese. I mention this because I am guessing that the questioner reads Chinese as a first language.
Please also note that curiousdannii has already drawn attention to NSM in connection with this question. Dominik Lukes (above) also has referenced Anna Wierzbicka who is the originator of NSM theory as it now stands. She in turn acknowledges a former teacher of hers, Andrzej Bogusławski who has also worked with her to develop the theory. The intellectual roots of the ideas go back a long way. Seventeenth century thinkers like Gottlieb Leibniz and John Locke had significant philosophical input into the background of the theory. Anna Wierzbicka and Cliff Goddard are leading proponents now, having put together the table of virtually all of the proposed semantic primes between them, so I understand.
You would have to explain what you mean by "universal". Some people use it for anything found in enough languages that it cannot have arisen by chance (but there can be counterexamples) -- this is the Greenbergian statistical sense. It could be restricted to any so-far un-contradicted generalization about all languages such as that no language has more nasal vowels than oral vowels. Then such generalizations have to be distinguished in terms of the explanatory mechanism.
Many supposed observational "universals" are epiphenomena that arise from more general facts about the world, and aren't part of a specific faculty of grammatical computation. (Some people simply deny that there is any cognitive faculty that is specific to language, so no further conversation is possible with them). In OT, for instance, it is usually stipulated that there is a constraint penalizing syllables without onsets and another that penalizes syllables with codas (Ons and *Cod) -- the "universal" content is that there is no constraint penalizing syllables with onsets, and no constraint penalizing syllables without codas (no Cod and *Ons). However, the observational "universality" of Ons and *Cod can be derived from non-grammatical facts about perception (meaning that the constraints can be learned rather than stipulated as part of a pre-set toolkit). When referring to "universals", folks with an interest in universal grammar tend to specifically mean those things that are part of the universal grammar computational apparatus.
Talmy points to a semantic principle of magnitude neutrality for closed-class words, to the effect that The ant crawled across my palm and The bus drove across the country won't be encoded with different prepositions reflecting the distance. This would be an example of an epiphenomenal semantic universal arising from factors that are outside of grammatical computation. (Talmy is not known to be an advocate of the concept "grammatical computation"). As far as semantic universals in the strong grammatical sense are concerned, it's difficult to establish that there are any, as opposed to truths that follow from more general cognitive properties. People can understand each other, because meaning is a relationship between linguistic form and states of affairs that can be perceived, and with a bit of word, we can all use out perceptual apparatus to understand what state of affairs "My shaved cat was followed by three bears" refers to, even if we have no experience with cats, shaving, bears, or passive constructions.
If you Google on "semantic universal", you'll get plenty of hits. Here's a paragraph from Wikipedia: Linguistic universals in semantics. In my opinion, apart from matters closely tied to human sense perception, there aren't any. Language translation can be done syntactically, without reference to semantics.
By "matters closely tied to human sense perception", I mean colors and perhaps other similar things. See Basic Color Terms. The names for colors really do have semantic reference to what things in the world stimulate the rods and cones in our eyes, and they can't be adequately described by syntactic relationships among linguistic descriptions (as many things termed "semantic" can be).