Q. Paul writes to Timothy, “We have put our hope in the living God, who is the Savior of all people, and especially of those who believe.” Universalists use this as a backing for all being saved. What does Paul mean when he refers to God as being the “Savior of all people,” and why does he add “especially of those who believe?”
I think what Paul means is that there isn’t any other Savior for people. His statement here is equivalent to what Peter tells the Sanhedrin when they want him to stop preaching in the name of Jesus: “Salvation is found in no one else, for there is no other name under heaven given to mankind by which we must be saved.” So different nations or cultures aren’t saved by different gods; the living God (that is, the only God who truly exists) is the one that all people must look to for salvation.
But this God is the “Savior” in a more specific sense of those who already believe in him and have found salvation. That’s why Paul adds, “especially of those who believe.”