To start with, you're not understanding what Sola Scriptura actually means. It does not mean that only explicit propositions found in the scriptures are accepted. It does not mean that Protestants reject or ignore tradition, historical theology, creeds, or reason. Sola Scriptura means that Protestants think that the scriptures are the only infallible source of knowledge on this side of resurrection (on the other side we will be able to speak directly to God of course.) Sola Scriptura means that when there are questions and debates, the highest authority we can appeal to is the scriptures. But it doesn't mean the scriptures contain everything we want to know, nor that all of the scriptures are easy to understand. We interpret the scriptures under the power of the Holy Spirit, guided by generations of past Christians, using the fullness of the intellects God has granted to us.
So there's nothing to reconcile. Like the Apostles' Creed, Nicene Creed, and Chalcedonian Definition, the Athanasian Creed is believed by most Protestants to be an accurate summary of the theology taught by the Bible. Protestants can recite it and join the other Christians around the world who share its truths. And some Protestant denominations would endorse it as an authoritative summary of their beliefs. This does not make it part of the canon, nor does it ever sit in a higher place than the scriptures. Any Protestant church which truly believes in Sola Scriptura would allow in principle for the possibility that a deeper understanding of scripture may convince them that some aspect of the Athanasian Creed needs revising, although after all this time they'd consider that unlikely to happen.
(There is some small disagreement over some lines already, in particular the first and last. Many Protestants would disagree that doubt precludes salvation. And of course "descended into hell" is disputed by many as it is in the other creeds, but that is more an issue of translation.)