God certainly is the One who gave us life and the means to sustain that life, so He has claims over us for those reasons alone. Yet people who live in denial of God's rights over us think they can take the perks without being responsible to God for them! I think God would care about that. Yet such people don't escape their responsibility just because they deny God! This was expressed by former atheist, C.S. Lewis, like this:
"A man can no more diminish God’s glory by refusing to worship Him than a lunatic can put out the sun by scribbling the word, ‘darkness’ on the walls of his cell." He also said,
"God cannot give us a happiness and peace apart from Himself, because it is not there. There can be no such thing." Plus, "There are only two kinds of people in the end – those who say to God, ‘Thy will be done’ and those to whom God says, ‘Thy will be done'." [Mere Christianity] All of the people who either don't believe God exists, or who live their lives without any reference to God, are going to care about their rejection when God's judgment comes. And it's coming, because the God of the Bible is Righteous, and Just, and Holy. He has promised to "bring to ruin those ruining the Earth" and to render justice on a cosmic scale. It's time we started caring.
If you want to be able to call God your heavenly Father (as well as your Creator), you have to be adopted into His heavenly family, by the new birth. That is a work of the Holy Spirit. The Bible alone shows how that happens and how God has already done everything we cannot do to rectify the alienation between us and Him, due to our lives of rebellion against Him. It matters not what religion you are just so long as you become His child by faith, for simply being one of His creatures will not save you from His righteous and holy judgment.