Protestant answer. Simply, the Athanasian Creed is not Scripture. It is a 'doctrine of men'. We must be careful not to substitute man's teachings for God's, as the Pharisees often did. Creeds are useful summaries of the articles of our faith, and can serve as a litmus test to root out belief in false teachings, to prevent those who believe such from ascending to positions of leadership. But creeds not found within the text of Scripture should not be treated with the authority of Scripture.
Paul the Apostle teaches in New Testament Scripture:
If you declare with your mouth, “Jesus is Lord,” and believe in your
heart that God raised him from the dead, you will be saved.
Romans 10:9, NIV. No mention of the doctrine of Trinity here. Jesus is the Way.
Some things are implied here:
- Belief in the God of Israel, the one true God
- The God of Israel (not any other) raised Jesus from the dead
- This confession is public, "with your mouth", not private, in your heart only
- (By the way, 'Lord' in this verse is not the Divine Name and is not equivalent to 'Messiah'; it is a synonym for 'master'. Your confession is to Jesus' authority over you.)
Additionally, repentance as a precondition for salvation was taught by John the Baptist, Simon Peter and the other apostles. (For those two we have quotations of them teaching it.) Paul also taught the baptism of John which follows repentance to his student Apollos. He just doesn't mention it in this verse in Romans.
Peter replied, “Repent and be baptized, every one of you, in the name
of Jesus Christ for the forgiveness of your sins. And you will receive
the gift of the Holy Spirit. The promise is for you and your
children and for all who are far off—for all whom the Lord our God
will call.” With many other words he warned them; and he pleaded with them,
“Save yourselves from this corrupt generation.”
Acts 2:38-40, NIV. Jesus affirms that repentance is required for salvation in his famous dialogue with Nicodemus the judge. "Born of water and the Spirit" refers to the baptism of John; 'born of water' referring to literal immersion in clean water, and 'born of Spirit' referring to repentance as a means of spiritual purification.
Jesus answered, “Very truly I tell you, no one can enter the kingdom of God unless they are born of water and the Spirit. Flesh gives birth to flesh, but Spirit gives birth to spirit.
John 3:5-6, NIV. It could be argued what level of understanding of John's baptism is required for it to be an earnest thing. In my opinion, it is sufficient that baptism is accompanied by genuine repentance, given how John and Peter preached; but that is only my opinion.
But to my recollection, no Scriptural source teaches that belief in specific teachings about the Holy Spirit, including Trinity, or even awareness of such, are essential to salvation.