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Is there any site where I can find the list of natural languages that dont have a list of phonemes?
I want to discover the minimum amount of vowels needed to make sure each natural language has at least one vowel at this list of vowel phonemes (will deal with consonants later) and to do this I need a place where I can find the languages that dont have any vowel from a list of vowels.
There is not such a site. Also, a site might have a list but a language doesn't have a list. Maybe you mean that the language has phonemes, which you could put in a list. All spoken languages have phonemes (signed languages have cheremes). We know the phonemes of e.g. many dialects of Finnish; we do not know any of the phonemes of Sentinelese (we don't know anything about the language). I think therefore you don't mean "what language are we ignorant of", you must mean "what sounds are present in all human languages".
Asking about phonemes is asking for trouble because there is zero agreement as to whether phonemes have any physical properties. For example, "a" is a common indispensible vowel in many languages, but in Arabic it is pronounced different from how it is pronounced in Swahili. At the level of physical realization, there is no vowel such that that realization is systematically part of every human language. But we typically classify the vowel that is in that general region as "/a/". Marshallese clearly has the pronunciation [i], but that is arguably a phonetic property of a more abstract vowel that is simply "high", not front, back or rounded.
The only way in which it make sense to compare physical realization of two sound tokens is via identity of acoustic properties. You would need to include enough properties that the phonemes of any human language can be identified, for example you can't just use F1-F2 because you would not detect tonal distinctions which exist in almost half of the languages of the world. Since males and females, adults and children speak languages, a statement about the physical properties of "/a/" in Finnish has to be something true of all speakers of Finnish (there is no such absolute unity). Hopefully it is clear that there is no set of physical properties that are universally present in all human-spoken outputs.
Given the options of focusing on physical realization versus analytic conventions (phonemes), I think the physical-realization approach is most hopeless. There is a theoretical way to approach the question in terms of phonemes, which is founded on the idea of auditory standards as embodied in the IPA. Linguists have managed to make such judgments (not always well-informed), based on determining that a given sound is closest to IPA [e] (as opposed to [ɪ, ɛ] and so on). Analysts go off the rails in a couple of ways, one being orthographic convenience (typing ɜ rather and e might be a nuisance), the other being analytic (if it phonologically patterns with high vowels, should you not write [i] rather than [e]?). Since we don't agree on these issues of phonemic analysis, we also don't agree on what phonemes exist in the languages of the world.
The problem is, phonemes are difficult to compare between languages. For example, English is usually said to have /t/ (realized as aspirated) and /d/ (realized as unaspirated and weakly voiced). When comparing its phonemes against, say, Sanskrit, is it accurate to say that English lacks /tʰ/? Or, if you decide that English has phonemic /tʰ/, does it lack /t/? Or /d/? It certainly doesn't seem to have three separate stop series.
Vowels make it even harder. Unlike the space of consonants, the space of vowels is completely continuous. You can find an intermediate vowel between any two others, and most vowels used in actual speech don't line up perfectly with any of the IPA symbols. So even if a phoneme /i/ is always realized as a high front unrounded vowel, "high front unrounded" can be pretty broad. If one language has two low vowel phonemes, /æ/ and /ɑ/, and another only has a single low vowel /a/, I can guarantee you there will be overlap between their realizations—the difference isn't in which vowel sounds they use, but in the nature of the contrast.
So for comparisons like this, it might make more sense to talk about what contrasts are most common. For example, I don't know of any language that doesn't contrast high vs low vowels, but I can think of some that don't contrast high vs mid, or front vs back.
