If God must first work in a person before that person can then obey the gospel, then you are putting fault, blame, culpability upon God for all those that do not obey the gospel.
God had begun that good work in those Philippians for they had first obeyed the gospel. The gospel tells man to believe and when men believe then God is working in them. Not the other way around, God does not first work in a person to enable that person to believe. You say yourself " it is God who begins the good work in believers" God works in those that ALREADY believe.
Again, some of those in Galatia had left the gospel, Gal 1:6,7 and God was no longer working in them. God worked in them for keeping the gospel and quit working in them when they quit obeying the truth/gospel, Gal 3:1; 5:7.
No, I didn't and that doesn't automatically mean that. Human live in sins and enjoy sins until God starts the work. When God starts the work, the live of the saved men maybe two steps forward and three steps back, but the difference is that men do no longer enjoy sins, instead he hate himself in falling to the sins.
You are wrong, the obedience of the Phillipians to the Gospel is the proof that God is working in them. You are accursed, sorry. It was Paul who said that, inspired by God, that it was God who begins the work in a man. The resurrection of Lazarus by Jesus describes the issue greatly. When Lazarus is dead, can Lazarus hear the word of Jesus? Will Lazarus response and believe in Jesus? No, Jesus had first supernaturally resurrected Lazarus then He call Lazarus to come forth. The same case with sinner, sinners are dead in spirit and will not come to God. Holy Spirit start the works in men by 'resurrecting' the spirit of men and only then He call men to repent and believe. That's the full gospel.
I read Galatians chapter 1, 3 and 5. None points out your conclusion at all. In contrary, such men were actually never been saved to start of with, as mentioned in 1 John 2:19. So again, your claim is contrary to what Paul said in the Philippians and may be blaspheming God. God will not fail the Good Work that He has started on the men He saved. But according to your false gospel, God worked in some men for keeping the Gospel but later on quit working in them just because they quit. That tells much that the god you worship is a weak god. My God is not weak. He is omniscient and omnipotent, and once He started the Good Work in a saved men, He will make sure that He will finish such Good Work as well.
May the Lord's mercy be upon this forum