The ontological argument for God's existence often is attributed to Anselm of Canterbury (circa 1033-1109 CE). If by "argument" we mean a systematic and developed case made for a belief or set of beliefs, then yes, Anselm might be credited with the first theistic argument based on the concept of perfect existence. However, I believe the roots for the ontological argument can be found in writers like Cyprian of Carthage. For instance, he writes:
"To God who alone is, belongs the whole name of God;
therefore He is one, and He in His entirety is
everywhere diffused. For even the common people in
many things naturally confess God, when their mind and
soul are admonished of their author and origin. We
frequently hear it said, 'O God,' and 'God sees,' and
'I commend to God,' and 'God give you,' and 'as God
will,' and 'if God should grant'; and this is the very
height of sinfulness, to refuse to acknowledge Him
whom you cannot but know" (On The Vanity of Idols 9).
I have yet to see an author make this connection although someone has possibly associated Cyprian with Anselm before. I'd like to advance this idea to see if it can float.