The issue is, as you stated, which is first salvation or faith, but you never answered the question. Why did God choose Abraham when he was still an idol worshiper and, therefore, had no faith?
Your statement of faith being the reason for Abraham's justification is true but your application of it to my question is anachronistic, and, therefore, doesn't apply.
My question is not dealing with Abraham's being credited with righteousness (his faith was counted as righteousness). My question is dealing with God's choosing him when he was faithless.
God chose Abraham because God through foreknowledge knew Abraham would believe. Election follows God's foreknowledge as plainly shown in scripture.
1 Pet 1:2 Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied.
This verse here clearly explains that election is based on something God knew beforehand. If it were not faith, then what would it be?
And Jesus knew exactly "from the beginning" who would believe not, and therefore he also knows who will believe. This is not my opinion, this is declared in scripture.
John 6:64 But there are some of you that believe not. For Jesus knew from the beginning who they were that believed not, and who should betray him.
So, we see from scripture itself that Jesus knows who will believe and who will not. And he knew this "from the beginning".
Calvinism turns this around 180 degrees and says God first chooses or elects a man, and then regenerates him. The scriptures nowhere say that or show that. In fact, in the parable of the marriage, it is shown that those who answer God's call in obedience and come to the marriage with the proper wedding garment (Christ's righteousness) are the chosen or elect.
Matt 22:2 The kingdom of heaven is like unto a certain king, which made a marriage for his son,
3 And sent forth his servants to call them that were bidden to the wedding: and they would not come.
4 Again, he sent forth other servants, saying, Tell them which are bidden, Behold, I have prepared my dinner: my oxen and my fatlings are killed, and all things are ready: come unto the marriage.
5 But they made light of it, and went their ways, one to his farm, another to his merchandise:
6 And the remnant took his servants, and entreated them spitefully, and slew them.
7 But when the king heard thereof, he was wroth: and he sent forth his armies, and destroyed those murderers, and burned up their city.
Here, the king is God the Father. His son is of course Jesus. He called men to come to the wedding. It was his will and desire that they come. But they refused.
This first part of the passage speaks of the Jews. Jesus was first sent to God's chosen and elect people.
Matt 15:24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
The Jews were God's elect and chosen people. But they forfeited their election through unbelief. But not all, a remnant did believe and continued to be God's elect.
Rom 11:1 I say then, Hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin.
2 God hath not cast away his people which he foreknew. Wot ye not what the scripture saith of Elias? how he maketh intercession to God against Israel, saying,
3 Lord, they have killed thy prophets, and digged down thine altars; and I am left alone, and they seek my life.
4 But what saith the answer of God unto him? I have reserved to myself seven thousand men, who have not bowed the knee to the image of Baal.
5 Even so then at this present time also there is a remnant according to the election of grace.
6 And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then is it no more grace: otherwise work is no more work.
Here it is clearly explained. God did not cast away all the Jews. He knew that seven thousand would not bow the knee to Baal. These were those faithful Jews who trusted in God. And it directly says there is a remnant according to the election of grace, and explains that they are elect through God's grace and not according to works.
And grace is through faith.
Eph 2:8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
You receive God's grace "through faith". You must first have faith before you can receive grace.
Rom 4:16 Therefore it is of faith, that it might be by grace; to the end the promise might be sure to all the seed; not to that only which is of the law, but to that also which is of the faith of Abraham; who is the father of us all,
Rom 5:2 By whom also we have access by faith into this grace wherein we stand, and rejoice in hope of the glory of God.
So, God the Father could see down through time and see those who would be faithful and believe in him. And it is these who he foreknew that he elected.
Back to the wedding, we see that only those who obeyed God's calling and came to the wedding were the chosen or elect.
Matt 2:14 For many are called, but few are chosen.
The doctrine of Limited Atonement is false. Jesus died for all men, and God calls all men through Jesus. Any man can choose Christ if he so desires. And God the Father already knows who will believe on his Son, and it is these that are his elect.
And it is not set in stone. One who is not elect now can become elect.
Rom 11:19 Thou wilt say then, The branches were broken off, that I might be graffed in.
20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:
21 For if God spared not the natural branches, take heed lest he also spare not thee.
Rom 11:23 And they also, if they abide not still in unbelief, shall be graffed in: for God is able to graff them in again.
The Jews are the natural olive tree spoken of here. They are the chosen, the elect. But because of unbelief they have been broken off (vs 20). And us Gentiles who have believed have been graffed into this tree. But we are called the wild olive tree in Rom 11:17.
But notice very importantly in Romans 11:23 that Paul says if the Jews that are at present broken off from the natural tree turn from unbelief and trust in Christ, then God is able to graff them back into the natural olive tree "again". They can become the elect once again.
Rom 11:24 For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree?
So, God has not determined who will believe and who will not. God does not first elect someone and determine they will be saved. No, God through foreknowledge can see who will believe, and these are the elect.
And a man who is not elect at this moment because of unbelief can turn from unbelief to trust in Christ and become the elect.