We can claim to be one of the elect after having been saved by the grace of God!
Exactly, it is the only way you can know your elect.
God preserves the lives of His saints. That includes those He foreknew as His own.
Since all things work to their good, but the elect must believe in the gospel, it is also the reason for why Paul labored in preaching and was willing to suffer for the sake of Christ.
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2 Timothy 2:10
Therefore I endure all things for the sake of the elect, that they also may obtain the salvation which is in Christ Jesus with eternal glory.
The elect must be saved. The elect must obtain salvation, and they will. With God when he speaks something into existence, it must occur as He has said, it is also why prophecies come from God are always true. Before I was saved, I had God's judgement of wrath on me for my sins, but God had another plan for my life. He preserved my life until in the fulness of my time, He revealed Christ in me.
Galatians 1:14-16
New King James Version
14 And I advanced in Judaism beyond many of my contemporaries in my own nation, being more exceedingly zealous for the traditions of my fathers.
15 But when it pleased God, who separated me from my mother’s womb and called
me through His grace, 16 to reveal His Son in me, that I might preach Him among the Gentiles, I did not immediately confer with flesh and blood,