How can God be three Persons when He is defined by thousands of singular personal pronouns, which define ONE Person?
The problem is not existential but definitional. God exists and is a certain way. We can define "person" to exclude God's Trinitarian nature as a logical possibility, or we can define "person" to include both human persons and the three Divine persons. The Church has chosen to base the definition of person on God and humanity, not on humanity alone. It recognizes multiple aspects of personality as already understood by human philosophers in the Father, Son and Holy Spirit, where they are shown in Scripture to be distinct persons.
At the same time, there is a unity among the persons of the Trinity that no group of human persons has between them. Our unity as individuals does not extend to incorporate other persons. God's does. That makes God very different from us, in a category by Himself.
The Bible says that when a man and women marry, they become one flesh. This unity is limited but real. Perhaps if Adam and Eve had not eaten from the tree of the knowledge of Good and Evil before consummating their marriage, human marriages, families and even all of humankind would have had such unity as God always has? This insight gives us the answer.
How can God be three persons yet be one God? Because He never sinned. Sin brings division. Division cannot occur unless there was a preexisting unity.
Unity is the original state of being. Our separation from one another not just in personhood but in love, communion and fellowship, that is what needs explanation.