Self Existence of God

And God said unto Moses, I AM THAT I AM: and He said, Thus shall thou say unto the children of Israel, I AM has sent me unto you. Exodus 3:14

But our God is in the heavens: He has done whatsoever He has pleased. Psalms 115:3

Whatsoever the LORD pleased, that did He in heaven, and in earth, in the seas, and all deep places. Psalms 135:6

Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am. John 8:58

I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty. Rev 1:8

The Hebrew word for I AM is 'Eh^eYeh.

OT:1961 hayah

(haw-yaw); a primitive root [compare OT:1933]; to exist, i.e. be or become, come to pass (always emphatic, and not a mere copula or auxiliary):

KJV - beacon, X altogether, be (-come), accomplished, committed, like), break, cause, come (to pass), do, faint, fall, + follow, happen, X have, last, pertain, quit (oneself-), require, X use.
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)

The Greek word for I AM is Eimi.

NT:1510 eimi

(i-mee'); the first person singular present indicative; a prolonged form of a primary and defective verb; I exist (used only when emphatic):

KJV - am, have been, X it is I, was. S
(Biblesoft's New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright (c) 1994, Biblesoft and International Bible Translators, Inc.)