Ephesians 2:5 Paul made clarification, how one get saved " by grace ye are save' hence referring also to eph. 2:8 which is 'through faith'. So the verse is not saying regeneration before faith, rather faith to be saved.
In my Bible, verses 1-5 come before verses 8-9. This means the Apostle was laying the groundwork in the earlier verses. He begins by introducing the term quickened and the phrase dead in trespasses and sins.
Quickened is easy. That simply means gives life to. Dead in trespasses and sins is what he explains for the next 2 verses. Pretty much the description is dead, being dominated, and doomed. But presto, God intervenes and viola...He takes dead people and makes them alive.
Dead people are unbelievers. That means they don't as yet have faith. God even, with us in this estate, makes us alive together with Christ. By the time we come to verse 8, God is simply giving more details about how He makes us alive.
So, still have God making people alive when they were still unbelievers.