There are many facets to this topic. Broadly speaking I think we can separate them into two categories, Hashem Himself, and our connection to Him. I’ll address the second one (first). According to your understanding, we can connect to Him on two levels, A) through ‘imitating’ His attributes, since it is using the same Sefiros (Tanya part 1 ch. 2-3). B) Through emunah which is unique to us Jews. You further correlated these two concepts to the two mitzvohs, Yedias Hashem and Emunah. “Knowing” Hashem by definition can only be actualized by things that we can envision, whereas emunah is believing in Hashems ‘essence’ something that no human can actually “know”. (It is this point which is the first category that I mentioned above).
There are a few points which I think you have misunderstood. Let’s start with the connection through ‘imitating’ His attributes. As mentioned above, you equate this with the mitzvoh of ‘knowing Hashem’ and you further claimed that in this regard the gentiles can also ‘know’ Hashem. I think you have a fundamental misunderstanding of what the Torah means by וידעת היום, והשבית אל לבבך וגו’, this mitzvah of Yediah does NOT mean simply understanding through logic (which is what a gentile can do as well). Furthermore I believe that this misunderstanding is why you also misapprehend what the mitzvah of emunah is.
The Tzemach Tzedak in mitzvahs Emunah ch. 3 explains what yediah actually means. In truth, the Tanya states this all the way at the start in ch. 3, and in Torah Ohr Mishpatim the first Drush. In a nutshell, all three of the first three Sefiros (Chabad), are unique. Chochmah and Binah are the intellectual faculties, i.e. what we use to actually reason with, however just knowing something does not change a person in the slightest. It is the third Sefira, Daas, which does this. Daas is what the person uses to connect his knowledge with himself.
[The Rashab in hemshech 5772 part 1 explains it succinctly. A person may know that a certain food or item is good, however as long as he doesn’t take HIMSELF into the equation, i.e. which is good for him, his knowledge of the item would not cause him to do anything about it].
Knowing the omnipotence of Hashem in all its intricacies, does not do anything for the person, he stays the same as he has always. However when he goes to the next step through meditating on these concepts and how they relate to HIM, that changes the person.
Now let’s take this a step further. What happens through this meditation, and why it effectuates a dramatic change is because through this we can actually ‘feel’ Hashems presence. To elaborate on this point would take up too much time, so a brief explanation will have to suffice for now. Because the Nefesh Elokis is made of the same ‘substance’ of (a certain level of) Hashem [this point needs serious elaboration for a different time], it is naturally drawn to Him, however the physical world prevents it from ‘connecting’ to its source. However, as the Baal Shem taught (that is what the Tanya means in part 2 ch. 1 see Likutei Sichos 29, p. 26) all physical entities’ existence is only from the Ohr that lies within it, which is directly from Hashem. Therefore, Chassidus teaches that when used correctly (Tanya p. 1 ch 7-9) one CAN connect to Hashem through the physical itself. But again, this only happens BECAUSE of Ten Sefiros that lie inherently in a Jew.
In other words, the world is full of opportunities to see Hashem in literally everything, as long as it done in the correct way, i.e. to draw closer to him. This ability is inherent ONLY to Jews because of where their soul comes from. Although a gentile may be able to understand (certain concepts) of Yechid Hashem, the next step, i.e. internalizing it, that is an ability ONLY a Jew has. (see Tanya p.1 ch 1, and chs. 18-22).
This, in a nutshell, is what the Mitzvah of Yedias Hashem is.
Emunas Hashem is a totally different mitzvah. It means believing the parts of Hashems’ Omnipotence that we cannot logically understand. And, by definition, being that we cannot understand it, we can also not internalize it in any way that it will change us and bring us closer to Hashem.