If I believe that Jesus is the Son of God the same way that I believe that Vladimir Putin is the leader of Russia, have I fulfilled the conditions needed to be saved? Or is there more to belief than that?
We know that it doesn't fulfill the conditions, because the devil believes it. And we know that the devil believes it because when Jesus came into the world and began to confront the demonic powers of the Devil, they said out loud, "We know who you are. You are the holy one of God. You are the Son of God." So the Devil is absolutely orthodox in his belief in the incarnation of the Son of God in Jesus Christ. To believe in orthodox Christology is not to be saved. The Devil is very orthodox when it comes to his understanding of Christ.
So what is missing is not believing in the fact that Jesus is the Son of God but delighting in that fact, embracing that fact, and making Christ the treasure and the Lord of your life by surrendering to him.
In other words, "belief" is seeing him for who he really is, seeing him as infinitely valuable as the Son of God. It's not just acknowledging the fact that he is the Son but also seeing him as infinitely precious and valuable. Satan, on the other hand, does not view God as precious and valuable. He hates Christ and Christ is a threat to his own value.
But when the Holy Spirit begins to work in our lives we're not deceived like that anymore. We recognize that our value is nothing compared to Jesus' value. Instead, we just want to know him, be with him, enjoy him, follow him, and celebrate him. That transition—that change of heart, so that we are now looking away from ourselves to Christ and embracing all that God is for us in him—that is what faith is. That is what belief is. That is what saves.