As Borgh says, causa causans is Latin. For many Latin words and phrases, there is no single established pronunciation in English. You can be fairly certain that causa causans will be pronounced as four syllables where the first and third start with the consonant sound /k/, but for nearly every other part, there is more than one pronunciation that you might hear.
There are a few artificial systems that exist for the purpose of giving more or less definite rules about how to pronounce Latin as an English speaker. According to one such system, which Wikipedia calls the "traditional English pronunciation of Latin" (that title is a little misleading because it only represents one tradition, and other traditions have coexisted with it for much of the duration when it was used), causa causans is pronounced /kɔːzə kɔːzənz/, "CAW-zuh CAW-zuhnz". As a rule of thumb, the pronunciation of Latin words in law or medicine often conforms to this system (there are exceptions).
Another system, the one which is more likely to be encountered by an English speaker who is taking a Latin course in school today, is referred to as "restored" pronunciation. This is an approximation using English sounds of what scholars think Classical Latin sounded like. The pronunciation of causa causans according to this system is /kaʊsə kaʊsɑːns/, "COW-suh COW-sahnce".
However, most English speakers don't actually learn, let alone follow, either of these systems, so in practice you'll hear pronunciations that mix and match features from these in not entirely systematic ways. For example, I would be completely unsurprised to hear /kaʊzə kaʊzənz/ "COW-zuh COW-zuhnz", where the vowel in the stressed syllable is pronounced as in the "reconstructed" system but the unstressed syllables are pronounced as in the "traditional" system; I can also imagine hearing variants like /kaʊzə kaʊzɑːnz/ and /kaʊsə kaʊsənz/.
If you were extremely interested in analyzing the reasons behind the use of all of these pronunciation variants, you might consider factors like the frequency of different spelling/sound correspondences in the rest of English or how the sound structure of these pronunciations compares to the sound structure of more frequent words, but I don't think the kind of analysis that a linguist would do would be likely to be useful to a learner in this case.
The practical advice I would give about how to pronounce such phrases is to follow one of the following strategies:
Don't worry about any of these specific words. Causa causans is so infrequent that rather than studying the pronunciation of this phrase in particular, you'd be better off spending the time improving your pronunciation skills in general by having conversations, listening, and so on. When you come to a difficult word like this, just use your intuition to guess how to pronounce it: I think the better your overall pronunciation skills are, the more likely it is that your guess will be similar to a native speaker's guess.
Pick one of the systems mentioned above (decide which one you prefer) and familiarize yourself with the basic rules, then use it whenever you run into a phrase that you recognize as Latin but that you haven't yet heard spoken aloud.
Try to listen to an English speaker pronouncing this particular phrase. This could be in person or using an audio file. There are a number of online tools that can help. I couldn't find causa causans in Forvo or Youglish but Youglish does have audio of people pronouncing causa in other contexts, which you might find helpful. For example, since the Latin phrase honoris causa is used in certain degree-awarding ceremonies, you can hear how some English speakers pronounce it: it seems to me that most speakers use /aʊ/, but I did also hear pronunciations with /ɔː/.
