A human being is very different to God, in almost all interpretations and views. So to say that a human could have 'cognition' of (I take it you mean, be aware of the existence of) a human by talking to them, and then to extrapolate that the same must be true of God, doesn't seem to hold true to me.
Conversing with God, i.e. interacting with God, or feeling the presence of God, or however you'd like to put it, is necessarily a very distorted experience. According to some, it may even be a hallucination, or fooling oneself, etc.
Lots of people believe themselves to have conversed with God. But so many of them come out of doing so saying God is different. They don't all come out with the same experience.
What's more, to say 'converse' with God necessitates that God can consciously return one's side of the conversation i.e. I talk to God, God talks back, is severely limiting the scope of this discussion by leaving out all the non-personal, or transpersonal, experiences and definitions of God, such as my own.