God said to Moses, “I AM WHO I AM.” And he said, “Say this to the people of Israel: ‘I AM has sent me to you.’” (Ex. 3.14 ESV).

Yeshua (Yeah shooa) is probably how people pronounced Jesus’ name in the first century. It was a common name, and the same as “Joshua” whom Moses named (see Num. 13.16). The name means “Jah saves.” The name “Yahveh,” of which Yah or Jah stands for the whole, is a form of the “to be” verb. When God spoke to Moses in the bush account, He named Himself “I Am” which states and means self existence. This is what Jesus claimed in Jn. 8.58-59: Jesus said to them, “Truly, truly, I say to you, before Abraham was, I am.” So they picked up stones to throw at him, but Jesus hid himself and went out of the temple (ESV). The Jews who picked up stones knew Jesus was claiming divinity. That Jesus claimed to be God was the reason they crucified Him: The Jews answered him, “We have a law, and according to that law he ought to die because he has made himself the Son of God.” (Jn.19.7 ESV). The Jews claimed to have a Law where death was the sentence for claiming divinity. Except, they actually don’t have a Law that states this at all. The closest I can come to identifying a section that possibly alludes to any concept like this, is where God answers Balak in Num. 23.19: God is not man, that he should lie,
or a son of man, that he should change his mind. Has he said, and will he not do it? Or has he spoken, and will he not fulfill it? (ESV). But this verse only contrasts God and sinful humans and says nothing about a man claiming divinity. It was God’s loving intention to enter His creation and save it: this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men (Acts 2.23 ESV).

God is life and always is. Here is a great article that traces the aspects of God’s essence and existence.

Doctrine in the Local Church: Aseity — Credo Magazine