FWIW, there actually is some Biblical basis, but it is overwhelmed by the verses that go the other way. See, for instance, Acts 3:21, John 1:29, Romans 5:18, Romans 11:32, 1 John 2:2, 1 Timothy 4:10, and Acts 17:22
Okay, let's look at those one at a time and see if it really addresses universalism
21
Heaven must receive him until the time comes for God to restore everything, as he promised long ago through his holy prophets. Acts 3:21
This doesn't suggest to me universalism, but it does suggest that God restores creation to its original intent one day at the end of time. He will do that with a new earth and a new heaven.
John 1:29
9
The next day John saw Jesus coming toward him and said, “Look, the Lamb of God, who takes away the sin of the world!
This needs to be taken in its context. We know that all did not receive him as it says in this same chapter in verse 12. But, to the ones who do receive him he gives the right to become children of God
18
Consequently, just as one trespass resulted in condemnation for all people, so also one righteous act resulted in justification and life for all people. Romans 5:18 This is close, but again the important thing is context. The one act of righteousness results in justification for all people who call upon him. Again, not all people will call upon him.
Romans 11:32 32
For God has bound everyone over to disobedience so that he may have mercy on them all.
needs to be read in context. The whole chapter starts by talking about Israel and the hardening that is presently going on in their hearts and the open door to the gospel experienced by the Gentiles
1 John 2:2
He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world.
He is the only atoning sacrifice. He was the only one qualified in all of creation to be our sacrifice, but not all will accept that. To those who don't, only eternal punish waits
1 Timothy 4:10
That is why we labor and strive, because we have put our hope in the living God, who is the Savior of all people, and especially of those who believe.
This being said, he is the only Savior because there is not other way. Jesus described himself as the way the truth and life. Yet, not everyone will accept their need for him or humble themselves to come to him. That is the essence of sin. That we think we can find our own way without him
Acts 17:22
22
Paul then stood up in the meeting of the Areopagus and said: “People of Athens! I see that in every way you are very religious.
I'm not sure why you put this passage in your list. All Paul said was that they were religious.