Short answer: Yes!! It takes 'God' zero time to process.
And so if one uses the usual formula speed = distance/time, it works out to infinite speed.
If because I'm not sure this formula applies here.
Longer answer
About God I've no idea since I've lost His (Her/Its) contact details. But I saw a man — now deceased — who was generally recognized as saint, sage, God-realized etc.
About his reputation... its probably not relevant.
I will only comment on what I saw up close:
Zero Response Time
When I met him he was past 95. He died a few years later at 102. So physically he was old, shriveled, stooped over double, almost inaudible. And very very slow... in walk, in eating, in speech.
But on more careful examination, I noticed his responses were instantaneous. Usually it was very laconic – a sentence, maybe just a word.
But at his most laconic it could be just the barest raising of an eyebrow. So slight that only the person who had to receive, got it. The others saw nothing.
Yet the response was ready before the person asking had even finished. Sometimes it was noticed, many times not. He never bothered to drive it in.
His 'Philosophy'
He was in no way an author, teacher, guru, philosopher, etc.
Mostly if someone asked him questions on such matters he'd avoid or give a conventional answer.
On the few occasions when he would speak more personally, the maximum he'd reveal is: "God does everything".
And this brings me to the nub of your question
No Ego
I've read a lot about sages and spiritual personalities who had no ego. And always had the nagging doubt: Is it true? Or is this post-hoc mythologization?
This was the one man I've seen for whom it was obviously true: He was so obviously immersed in the truth of God does everything that he seemed to have direct processing-less access to the — as you call it — database of the universe-doers knowledge.
Since it was processing-less, it was instantaneous, or infinite speed.
Or to be more precise, in terms of Shannon's sampling theorem, his speed of responses was always faster enough than my observation/sampling speed, that it was observationally instantaneous.
What this implies for God... I've no idea since as I said I've no hotline to that person/being/entity.