Is there a theological basis for our trust in God? Yes. We can trust in God because He trusts in us even more.
Theologically, can we say that God believes in us? Does He trust in us - He who is perfect and we who are so sinful and weak? Can we say further that God hopes in us more than we hope in Him?
One theologian contacted me saying that we should not say this. That it sounds Pelagian, he observed. This is insightful because it could be interpreted to mean that we have all we need and now it is up to us. This also could be interpreted in a manner that calls to question divine omnipotence. But God does not hope in us because we have all we or because we are pretty good people. Quite the opposite - He trusts in us because of something He sees in our weakness. Nor does He trust in us because He has to - we are not necessary in any principle way. His trust is completely free. He trusts in us because He wants to and because of something He sees in us that we do not see.
What is it that He sees?
(1) Christ sees the glory of the Father in us. This is why He entrusted Himself to us as a helpless baby and as a vulnerable condemned man. We are created in the image and likeness of God -- and there is nothing we can do that can ever erase the image completely.
(2) Furthermore, the Son of God is so devoted to the Father, when He sees His Father's image, His gaze makes the image perfect. Jesus sees us and we become who we are. Jesus looks on us in love, and we discover the pathway to lay up riches in heaven.
(3) It is this gaze of love, and not our failures, that most defines our existence. If Jesus' love for us is the most definitive thing in our lives, He has good reason to trust in us.
In fact, He does trust in us. Not only did He entrust Himself to us during His visible mission, He continues to entrust Himself to us in the Eucharist, the Sacraments, in those He entrusts to our care, but especially in the poor. If he entrusts all of this to us, then He trusts in us. He trust in us then provides the theological basis for our trust in Him - because He trusts in us, we know we can trust that He will give us all we need, that we are not abandon, that He is with us.