Yes, God wants us to trust Him and His providence for our lives, but He also wants us to be seeking Him and His righteousness, drawing ever closer to Him and living in a righteous manner. Augustine comments on this:
The kingdom of God and His righteousness is our good which we ought to make our end. But since in order to attain this end we are militant in this life, which may not be lived without supply of these necessaries, He promises, "These things shall be added unto you." That He says, "first," implies that these are to be sought second not in time, but in value; the one is our good, the other necessary to us. For example, we ought not to preach so that we may eat, for so we should hold the Gospel as of less value than our food; but we should therefore eat so that we may preach the Gospel. But if we "seek first the kingdom of God and his righteousness," that is, set this before all other things, and seek other things for the sake of this, we ought not to be anxious lest we should lack necessaries; and therefore He says, "All these things shall be added unto you;" that is, of course, without being a hindrance to you: that you may not in seeking them be turned away from the other, and thus set two ends before you.
- Golden Chain 3624
The Kingdom of God and His righteousness are our goal and ultimate end. Yet, while we are on this earth, we need things of this earth to survive (i.e. food, clothing, shelter, etc.). In this passage Jesus is encouraging us not to get too focused on those things. We are supposed to be focussed primarily on the Kingdom and on living virtuously (righteously, persevering in charity despite the great temptations toward uncharitable action). We are not to worry about our bodily needs (but we are also not to ignore them). We are to be focussed on living righteously so that we may one day hear those great words: "Welcome into the kingdom, my beloved servant." What we need to worry about is: "Am I living my whole life the way God wants me to live? Does God approve of the motivations, intentions, and execution of my actions? Do I live in a manner that comports with the truth, with reality, with the way God designed people to live in this universe?"