This view of the intention of God in the creation leads John Owen to propose a (to my mind at least) distinctly 'Kuyperian' (or 'transformationist' - see here for a good quote on that sort of thing) approach to culture.
“…God would hereby instruct us both in the use that we are to make of his creatures, and the improvement that we are to make of the work of the creation unto his glory. For the first, it is his will that we should not use any thing as merely made and created by him, though originally for that purpose, seeing as they are so left they are under the curse, and so impure and unclean unto them that use them…but he would have us look upon them and receive them as they are given over unto Christ…This God instructs us in, namely, to look for a profitable, sanctified use of the creatures in Christ, in that [he?] himself ordered them in the very first creation to fall at length naturally under his rule and dominion, making them all by him."
So, if we want to glorify God in our use of the various elements of the old creation, we must view them as not just having been created by God, but as belonging specifically to Christ the Redeemer, as being intended for subjection to him in the new creation.
So what does this mean of non-Christian use of the creation?
"The whole mystery of laying the works of the old creation in a subserviency unto the new being hidden from many ages and generation, from the foundation of the world men did, by the effects and works which they saw, conclude that there was an eternal power and infinite wisdom whereby they were produced: but whereas there is but a twofold holy use of the works of the creation – the one suited unto the state of innocency, and the moral-natural worship of God therein, which they had lost; the other to the state of grace, and the worship of God in that, which they had not attained, - the world and the inhabitants thereof, being otherwise involved in the curse and darkness wherewith it was attended, exercised themselves in fruitless speculations about them…and glorified not God in any due manner, Rom. i. 21. Neither do nor can men unto this day make any better improvement of their contemplation on the works of creation, who are unacquainted with the recapitulation of all things in Christ, and the beauty of it, that all things at first were made by him. "
I think this means that Owen would, for example, argue against any concept of common grace, or natural law, providing a 'neutral zone' where Christians and non-Christians can meet to do social-political-cultural work. God-honouring use of the creation in all of these activities (whether painting, building a bridge, teaching geography, or writing a song) is only possible when creation is viewed as properly belonging to, and destined for, the Lord Jesus Christ. God wants us to look at and treat creation as being subject to him.
All from John Owen, An Exposition of the Epistle to the Hebrews, Vol III. 81-82.