Yes, but since that gift is available to everyone, it's a given. It's a baseline from which everyone starts.
"For it is by grace you have been saved, through faith" That entire process mentioned -- "being saved by grace through faith" -- is a gift from God. We didn't come up with it. God came up with it. Essentially it is saying that "the plan of salvation" is a gift from God. That plan is: "saved by grace through faith."
So, these verse don't really address to whom the plan is offered. The chapter in question is specifically referencing those already Christians to whom Paul is writing. On down in the chapter it applies this plan to those Gentiles or Jews who participate in it.
So, from THIS chapter we know only that it applies to those who participate in it. I don't know anyone who disagrees with that except (off the top of my head) universalists.
From elsewhere in scripture, Romans 8:29 - "Romans 8:29 NIV
For those God foreknew he also predestined to be conformed to the likeness of his Son, that he might be the firstborn among many brothers.
Peter says in 1Pe1 we are the elect 2 who have been chosen according to the foreknowledge of God the Father, through the sanctifying work of the Spirit, for obedience to Jesus Christ and sprinkling by his blood
Who are these elect whom God has foreknown and predestined? Paul spells it out, in my opinion, in Romans 8:
22 We know that the whole creation has been groaning as in the pains of childbirth right up to the present time. 23 Not only so, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for our adoption as sons, the redemption of our bodies. 24 For in this hope we were saved. But hope that is seen is no hope at all. Who hopes for what he already has? 25 But if we hope for what we do not yet have, we wait for it patiently. 26 In the same way, the Spirit helps us in our weakness.
It is those who were saved through this hope of redemption in Christ who are the "foreknown" in verse 29 of Romans 8.
And nothing will separate us from the love of God which is ours through Christ Jesus our Lord.
No everyone does not start out “saved”, everyone starts out lost (except those too young or unable in mind/spirit to understand).
We must be “born again”/regenerated by God through repentance and faith in what Christ has done!
Where does it say that It’s given to everyone? Would you say that God gives faith to an atheist?
Romans 12:3 For by the grace given me I say to every one of you: Do not think of yourself more highly than you ought, but rather think of yourself with sober judgment, in accordance with the faith God has distributed to each of you.
Peter was talking to believers there, not to atheists.
>>It's a baseline from which everyone starts.<<
But who is it that it comes from and increases or perfects our faith?
Hebrews 12:2 Looking unto Jesus the author and finisher of our faith; who for the joy that was set before him endured the cross, despising the shame, and is set down at the right hand of the throne of God.