Well, even Thomas Aquinas didn't believe that man could fully know God's essence - and he is about as Western as you can get. Summa Theologica:
I answer that, It is impossible for any created intellect to comprehend God; yet "for the mind to attain to God in some degree is great beatitude," as Augustine says (De Verb. Dim., Serm. xxxvii).
In proof of this we must consider that what is comprehended is perfectly known; and that is perfectly known which is known so far as it can be known. Thus, if anything which is capable of scientific demonstration is held only by an opinion resting on a probably proof, it is not comprehended; as, for instance, if anyone knows by scientific demonstration that a triangle has three angles equal to two right angles, he comprehends that truth; whereas if anyone accepts it as a probable opinion because wise men or most men teach it, he cannot be said to comprehend the thing itself, because he does not attain to that perfect mode of knowledge of which it is intrinsically capable. But no created intellect can attain to that perfect mode of the knowledge of the Divine intellect whereof it is intrinsically capable. Which thus appears--Everything is knowable according to its actuality. But God, whose being is infinite, as was shown above (Article 7) is infinitely knowable. Now no created intellect can know God infinitely. For the created intellect knows the Divine essence more or less perfectly in proportion as it receives a greater or lesser light of glory. Since therefore the created light of glory received into any created intellect cannot be infinite, it is clearly impossible for any created intellect to know God in an infinite degree. Hence it is impossible that it should comprehend God.
I answer that, The created intellect, in seeing the divine essence, does not see in it all that God does or can do. For it is manifest that things are seen in God as they are in Him. But all other things are in God as effects are in the power of their cause. Therefore all things are seen in God as an effect is seen in its cause. Now it is clear that the more perfectly a cause is seen, the more of its effects can be seen in it. For whoever has a lofty understanding, as soon as one demonstrative principle is put before him can gather the knowledge of many conclusions; but this is beyond one of a weaker intellect, for he needs things to be explained to him separately. And so an intellect can know all the effects of a cause and the reasons for those effects in the cause itself, if it comprehends the cause wholly. Now no created intellect can comprehend God wholly, as shown above (Article 7). Therefore no created intellect in seeing God can know all that God does or can do, for this would be to comprehend His power; but of what God does or can do any intellect can know the more, the more perfectly it sees God.
I answer that, God cannot be seen in His essence by a mere human being, except he be separated from this mortal life. The reason is because, as was said above (Article 4), the mode of knowledge follows the mode of the nature of the knower. But our soul, as long as we live in this life, has its being in corporeal matter; hence naturally it knows only what has a form in matter, or what can be known by such a form. Now it is evident that the Divine essence cannot be known through the nature of material things.
For it was shown above (Question 2, Article 9) that the knowledge of God by means of any created similitude is not the vision of His essence. Hence it is impossible for the soul of man in this life to see the essence of God. This can be seen in the fact that the more our soul is abstracted from corporeal things, the more it is capable of receiving abstract intelligible things. Hence in dreams and alienations of the bodily senses divine revelations and foresight of future events are perceived the more clearly. It is not possible, therefore, that the soul in this mortal life should be raised up to the supreme of intelligible objects, i.e. to the divine essence.
We can know of God by our intellect uniting with divine revelation, but only partially. As we grow in faith, hope and charity, we know more and more of God's essence. We can know the likeness of God based on sense perception and enlightened by divine revelation, but only in a limited sense in this world.
I would love to know who in the Western tradition "knows" God - and how they managed that.
(other than the saints in heaven of course)