As has been already pointed out to you, the immediate context shows us a question being asked and the question being answered.
Hermeneutically, we have nothing to suggest that the answer to the question was intended to sidestep the question itself and say something different, as your interpretation suggests. So it begs the question of why you would look for something other than a direct answer without contextual evidence to suggest it?
The straightforward, logical explanation that the question, “what are the works that God requires?”, is answered by “the work of God” is “that you believe in the one he has sent”, and requires nothing outside of the context to arrive at this conclusion. The implication of the “(this is) the work of God (required)” is a natural understanding in the context of the question posed.
Secondly, you err logically by suggesting that to fulfill the requirement of God means that God owes us simply because we did something. It does not follow that fulfilling the obligation necessarily means God is obligated because of that action, nor that we deserve or have the right to claim God “owes” us now. Merit is never the question, only trust/faith/belief that God will do what he promised, thus, “Abraham believed, and God counted it as righteousness.” God is obligated to himself, not because we’ve earned it, but because God who made the promise cannot lie!
Being Sovereign, God is only obligated to himself- that is nothing outside of himself, ie, us or our actions, can obligate God to do anything.
This is where Paul’s exposition in Romans 4 regarding the promise of God predating the law and Abram’s faith gives insight! God made a promise to Abram, which means God obligates himself to keep it else he becomes a liar.
It doesn’t mean the one believing that God will do what he says is deserving of anything, nor is it our action that forces God into a corner to do something contrary to his desires.
Doug