Not at all unnaturally, but very logically or better theologically does Paul relate this Psalm to the Lord.
Here's how.
Of course, Paul, no less than John, understands that the Son is the co-Principle of the Father in creation of the universe (Hebrews 1:2). Is He, the Son, the necessary [co-]Principle for the Father in this magnum opus: the creation of the entirety of this vastness of the universe with the invisible angelic hosts, infinite stars and galaxies, versatile forms of life from whales to microscopic organisms, down to molecules, atoms, quarks or bosons, and all those wonderful and fixed laws of nature like those of gravity or of thermodynamics?
Yes, of course He is necessary [co-]Principle, for otherwise we shall get an absurd mythology that the Father was yet not Father in His Eternity but only a Monadic God, then having been bored, decided to come out of the teenage bare-God-years and come to a maturity of fatherhood and, since it was impossible for Him to become a natural Father, for nobody could share His uncreated nature, created another person, of a different, created nature and called him "son", which made Him a "father". The son, surely seeing nobody but God (for there was not yet the universe), asked Him, "Hey, who are you, and who am I?" And God told him: "I am your Creator, but out of courtesy and out of my fondness for you, I say metaphorically that you are my "only-begotten" son, that is to say that I gave birth to you, but in reality, you must know that you are created; although, I ask you to call me not "my Creator", but for a better intimacy and familiarity, "my Father", ok?" "Yes, ok, my Crea...sorry, my Father! But now what? now I want to play!" And God the "Father" then decided to create also the universe and told the "son": "I will now create the universe and you will help me!" "But cannot you create it alone? I do not want to work, I want just to play!" And the God told him: "Of course I can create without you, what a question?! But to help me in creation of the universe is a reason for you to play, because, a) itself the creating is an amusing process, trust Me, when I was making you, I felt a real surge of creative powers! and b) the universe will become for you such an amusing plaything, with all its creatures, especially with humans who are the most amusing of all, for they will start doing all kinds of funny things (unfortunately also nasty stupidities), that will provide us an ample reason to laugh and amuse ourselves!" "Ok, then! Tell me how to help you and I will try my best!" And so then God and His created son started to create the universe, or more precisely, God started to create out of nothing alone (how otherwise!) and then the son was making some small adjustments at the God’s behest and instruction.:)
The Son is called "son" only because He is born from the Father and as born has the very same nature and that He is absolutely, ontologically necessary for the Father in the act of creation, which act is one act likewise belonging to the Father and the Son.
Now, if the act of creation of the entire vastness of the universe is necessarily a joint action, can any other divine action be not such and not a joint one? Impossible! Now, when Father subjects the "everything" to Christ does He or can He, the Father, perform this act of subjecting without His Son/Logos? - Impossible, as demonstrated above. Thus, even this subjection is Their, the Father and the Son's joint act. But was not the everything subjected to the Son from the very moment of its, the everything's, creation? Yes, it was subjected to Him just as it was subjected to the Father. But then, if Christ is the Son-incarnate, that is to say, the very uncreated Person of the Son who has adopted a human nature, how He, the co-Sovereign with the Father, can find Himself as not yet having everything under His subjection, but in the process towards achieving this status?
The only solution is that here we speak not about the uncreated Son/Logos qua His uncreatedness, but qua His created human nature. Yes, historically, in the history of the universal salvation till the Second Coming, the humanity will undergo a process of liberation from sin and death, and as many as will desire this liberation through Christ, will get it, and eventually all such humans will be enthroned together with Christ as adopted children of God, through Christ - the only natural Son. And this is a process, the process of healing the fallen and bruised human nature and perfecting it to the "to a perfect man, to the measure of the stature of the fullness of Christ" (Eph. 4:13). And to such victorious men the everything will be subjected only and exclusively through Christ, in whom and through whom they will defeat the powers of darkness, and thus even a human nature of created men will become a ruler of the entire universe, just like Christ's human nature is.
That is why the plural of the Psalms is transferred into the singular of Hebrews, because the plurality of the mankind can achieve this status of ruling over all only through one singular human - the Lord Jesus Christ, the Incarnate God.
Thus, the Logos is not subjected to the Father qua God, but only qua His God-manhood, that is to say, according to His human nature. Just like the Logos who is co-unbegan and co-eternal and co-unending with the Father cannot die qua Logos, but only qua His human nature, which He adopted for always, for after the Incarnation some two thousand+ years ago, God is no more bodiless, but in one of Hypostases, that of the Son, has also a human, created nature, including human body, and this is and will be forever so.
NB. Please do not downvote without leaving some useful Comment explaining why this answer was unhelpful to you, and how it could be improved.