That would make sense if God said, "I am
that I am"...
"I am that I am" is a misleading translation of the Hebrew phrase ehyeh asher ehyeh in Exodus 3:14.
The Hebrew word ehyeh (HYH/hayah) contains a Hebrew verb related to hawah (HWH) in the Divine Name Jehovah (YHWH). Both HYH (hayah) in ehyeh and HWH (hawah) in YHWH/Jehovah mean "to be" in Hebrew - just a slight difference in connotation. From NW ref. footnote on Exodus 3
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"“I SHALL PROVE TO BE WHAT I SHALL PROVE TO BE.” Heb., אֶהְיֶֽה אֲשֶֽׁר אֶהְיֶֽה (
ʼEh·yehʹ ʼAsherʹ ʼEh·yehʹ), God’s own self-designation; Leeser, “I WILL BE THAT I WILL BE”; Rotherham, “I Will Become whatsoever I please.” Gr.,
E·goʹ ei·mi ho on, “I am The Being,” or, “I am The Existing One”; Lat.,
eʹgo sum qui sum, “I am Who I am.”
ʼEh·yehʹ comes from the Heb. verb
ha·yahʹ, “become; prove to be.” Here
ʼEh·yehʹ is in the imperfect state, first person sing., meaning “I shall become”; or, “I shall prove to be.” The reference here is not to God’s self-existence but to what he has in mind to become toward others. Compare
Ge 2:4 ftn, “Jehovah,” where the kindred, but different, Heb. verb
ha·wahʹ appears in the divine name."
Please note that both hawah and hayah are verbs - all verbs require action. Jehovah is not simply stating that He exists - the action involves causing things to exist.
Note also that both hawah in the Divine Name Jehovah and hayah in ehyeh (Ex.3:14) are in the Hebrew imperfect verb state = action in progress not yet complete. Therefore Jehovah continues to cause things to be - as in the Creator.
The context of Exodus 3:14 reveals an aspect of ehyeh, namely: Jehovah is the fulfiller of promises. Specifically in this context, fulfilling the promise to Abraham, Isaac and Jacob as to the promised land. This is also a definition of the Divine Name Jehovah which is also in the context of Exodus 3:14 (in the Hebrew and correct English translations).