How does God intervene in our lives, does He? Good question. I would argue from what I think is the Catholic position that the daily evidence of both His existance and interaction with us is less obvious to us, rather than less present due to our own distractions and disconect from both God and His creation. Before the Fall, we are told Adam “walked with God” there was real evidence of His existance not simply from Adam’s “walks” but not being blinded by sin, and having our focus distracted from the gifts of life, and all the bounty of the world he experienced God in the manner we will eventually in heaven. We often take for granted the very air we breath, the food that grows up from the ground and the beauty that surrounds us, all a reflection of not only God’s love for us, but his providing for our every need. That is providing for us even though we sometimes reject Him by our disregard for Him or outright ignoring of Him.
While miracles, or supernatural interventions are sometimes overlooked, or seen as something that only happens in rare cases, I do think they occur every day, we just don’t see them, or expect them to be flashy and grand. Some mistake submitting ourselves to God’s will, spiritual growth, and learning to trust in God with expecting God to be our servant and give us the prosperity, or easy life that we suppose others have.
I think sometimes the challanges we face in our daily life and what appears to be a rejection of our petition can be a way to bring us closer to God by sharing in His (in the second person in the Trinity and His suffering for our Salvation) a gift and vote of confidence in our sonship.