Paul's letter was to those in Rome. So, the "us" Paul speaks to are to the Christians in Rome...Yes, I understand that it is expanded to mean Christians everywhere.
Romans 1:7
To all who are in Rome, beloved of God called to be saints: Grace to you and peace from God our Father and the Lord Jesus Christ
If by "us" you mean that God's unconditional love is referred to Christians ONLY due to the verse in Romans, I disagree. I quoted that verse to show that nothing can separate you from God--meaning no conditions-- but there are other verses that I could have quoted where the application would be for the whole world.
John 3:16 which I quoted twice:
"For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have eternal life".
Romans 5:6 says
For when we were still without strength, in due time Christ died for the ungodly. For scarcely for a righteous man will one die; yet perhaps for a good man someone would even dare to die. But God demonstrated His own love toward "us" in that while we were still sinners, Christ died for us....
John 3:16 says that God loved the world by giving us His begotten Son. We're told in Roman that God demonstrated His love for us while we were still sinners by allowing the death of His Son. It shows that He loved us even before we were Christians.
We're told again in Acts 17:22-31 of God's love--and while it does not use the word "love" in this passage, it demonstrate His love by reminding us of His Son's death.
22 Then Paul stood in the midst of the Areopagus and said, “Men of Athens, I perceive that in all things you are very religious; 23 or as I was passing through and considering the objects of your worship, I even found an altar with this inscription:
TO THE UNKNOWN GOD.
Therefore, the One whom you worship without knowing, Him I proclaim to you: 24 “God, who made the world and everything in it, since He is Lord of heaven and earth, does not dwell in temples made with hands. 25 Nor is He worshiped with men’s hands, as though He needed anything, since He gives to all life, breath, and all things. 26 And He has made from one blood every nation of men to dwell on all the face of the earth, and has determined their preappointed times and the boundaries of their dwellings, 27 so that they should seek the Lord, in the hope that they might grope for Him and find Him, though He is not far from each one of us; 28 for in Him we live and move and have our being, as also some of your own poets have said, ‘For we are also His offspring.’ 29 Therefore, since we are the offspring of God, we ought not to think that the Divine Nature is like gold or silver or stone, something shaped by art and man’s devising. 30 Truly, these times of ignorance God overlooked, but now commands all men everywhere to repent, 31 because He has appointed a day on which He will judge the world in righteousness by the Man whom He has ordained. He has given assurance of this to all by raising Him from the dead.”
BTW, the "us"/"we" in these verses are speaking to the Man of Athens (Acts 17:22), yes, I understand that it can be applied to us Christians.
His love is unconditional to all, it's not only for the Christian.