Is it possible for our hearts to encompass Allah swt? In other words can one experience God himself in his essence? If yes how would one do so? If no, how close can man get?

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No, of course, it is not possible, because it is not possible to encompass God, glory be to Him, but you can know how close you are to Him, glory be to Him, by the extent of your obedience to Him and your sincerity in your work and worship, then many things will be revealed to you.