According to Catholicism, how can the Holy Spirit proceed from the Father and the Son if it is God?

Given the Filioque (the idea that the Holy Spirit proceeds from the Father and the Son), how can the Holy Spirit be considered God? Given that God is necessary, it seems to me that the Filioque implies the Holy Spirit is contingent on the Father and the Son, but that means it’s not necessary. Am I misunderstanding the Filioque here? Can someone provide a way to solve this apparent contradiction?