No, there may not be any universal meanings. Here is an example. In most (maybe all) Bantu languages, there is no word for "hand" and no word for "arm", because there is a word meaning "hand and arm". The English word "dirt" refers to the stuff that you sweep up in your house, and the stuff you plant crops in: in Bantu languages, these are different words. Two words in different languages would have the same meaning if they referred to the same things, which is not the case. "Jump" in English covers jumping up (not down) and crossing (a stream, road) in Logoori. There are many kinds of "fall" in Logoori (catastrophic falling out of a tree vs. stumbling, etc).
The most likely candidates will be natural objects that are trivially distinguishable from other similar objects. Because bodies are continuous structures, body part divisions are somewhat arbitrary (as in the case of "arm" and "hand", also "leg" and "foot").
Swadesh lists are the best approximation that you will find, and they are usually clearly wrong on a number of cases for any language. You will have to give up on the notion of "all languages", but as a first step you could try to get the equivalents of a Swadesh list or the Leipzig list in some language, and perhaps try to add weights to indicate how close the other language word is to the English word (for example "water" as a noun, and only in the H20 sense, is pretty stable as to referent). Some of the words are ludicrous as candidates for universals, for example "if", which basically doesn't exist in Bantu.