The question appears to be whether there are any properties of human language which are directly attested in all human languages and "sufficiently similar" then one would say that they are essentially the same. But, this apparently should exclude anything that is arguably due to an innate property of the human language faculty, thus is intended to elicit examples of accidental universals (as stated, "this is different from the innateness hypothesis").
The best candidate that I know of is "mother, although even comparing [mʌðr], [mʊr], [matʲ], [ʔum] the similarity is not striking. When you factor in Finnish äiti and Georgian deda, it turns out that the statistically significant similarity of words for "mother" is still just a tendency and not an absolute universal.
You say that you do not care if humans are born with knowledge of a language, which I assume is a wording mistake since nobody claims that humans are born with knowledge of a specific language: the innatist claim is that humans are born with knowledge of general properties of all human languages, i.e. the architecture of the language faculty. An example of something that is true of all human languages, but something that is innate and not learned, is the fact that language is based on grouping smaller units of one type into units of a broader type, and so on up the tree. Example: groups of features form individual sounds; groups of sounds form morphemes; groups of morphemes form words; groups of words form phrases, groups of phrases form clauses, which group into sentences. This is the essence of the innatist hypothesis, which I assume you are setting aside in favor of accidental universal properties. There are none.