“For whom He foreknew, He also predestined to be conformed to the image of His Son, that He might be the firstborn among many brethren.”
‭‭Romans‬ ‭8‬:‭29‬ ESV

“Praise be to the God and Father of our Lord Jesus Christ, who has blessed us in the heavenly realms with every spiritual blessing in Christ. For he chose us in him before the creation of the world to be holy and blameless in his sight. In love he predestined us for adoption to sonship through Jesus Christ, in accordance with his pleasure and will— to the praise of his glorious grace, which he has freely given us in the One he loves.”
Ephesians 1:3-6 ESV

Foreknowledge

God foreknew us, He knew who would and would not be saved. Of those He foreknew would be saved, He predestined or predetermined that they would be conformed to the image of Christ. He didn’t pick who would or would not, but He did determine that those who would believe would be like Christ.

Eternal God

God is eternal. He is not bound by space or time. All of time, then, from beginning to end, from God’s point of view, is in an eternal now. God created time, is sovereign over it, He sees it, He’s within it, He enters it, He interacts and intervenes within it, all while being distinctly set apart from it. All of human history is happening all at once — past, present, and future. The entire Bible from Genesis to Revelation is happening right now as I type this, from God’s point of view. My entire existence, from conception to the eternal state, is now, so from God’s point of view, all who belong to Him are there with Him right now.
_{Genesis 1:1; Psalm 90:2; Psalm 139:16; Isaiah 57:15; Jeremiah 23:23–24; Isaiah 46:9–10; Isaiah 55:8–9; Daniel 4:35; John 1:14; Acts 17:27–28; Galatians 4:4; Ephesians 1:4; Colossians 1:16–17; 1 Timothy 1:17; Hebrews 4:13; 2 Peter 3:8; Revelation 1:8}

By this Ephesians 1:3–6 can be explained. He foreknew us and therefore chose us before the world was made, and knowing we need a Savior, the plan was already in place. From our point of view, everything had to play out in time, we had to respond and choose; from God’s point of view, it was already settled.

Lost Sheep

This does not have God choosing who gets saved and who does not, rather it has Him saving the known. God draws all men to Himself through the active work of the Holy Spirit. Christ’s death was for all; the invitation is for all who will, but God knows not all will. God pursues those He knows and has therefore chosen. The parable of the lost sheep comes to mind — the lost sheep is His already; it is not a wild sheep. This is why He actively chases it down. I once said to a friend, speaking of my journey toward salvation in Christ, “I was already His, I just didn’t know it yet.” _{Read my testimony.
Lost Sheep Parable: Luke 15:3–7; Matthew 18:12–14
My Sheep Know My Voice: John 10:27–29}

Apostasy

The question can be raised, “What about those who have fallen away? How can God foreknow someone’s salvation, and yet it still be possible for them to fall away and die in a lost state?”

Those He foreknew, the elect, are never at risk of dying in a lost state. The falling away spoken of refers to those who were never truly believers, never truly saved, to begin with. They may have believed they were, but true believers are not capable of apostasy. The parable of the sower comes to mind: the rocky and thorny soil represent a real-looking but ultimately false response or profession of faith; the tests, trials and distractions of life reveal the true nature of that faith. Only the good soil produces good fruit.

Summary

To summarize, God does not arbitrarily choose who is saved and who is not. He knows us and chooses those He knows will respond. Those He has chosen are His for eternity.
My sheep hear my voice, and I know them, and they follow me.  I give them eternal life, and they will never perish, and no one will snatch them out of my hand. My Father, who has given them to me, is greater than all, and no one is able to snatch them out of the Father’s hand.
John 10:27–29 ESV

“Who shall separate us from the love of Christ? Shall tribulation, or distress, or persecution, or famine, or nakedness, or danger, or sword? As it is written,

‘For your sake we are being killed all the day long;
    we are regarded as sheep to be slaughtered.’

No, in all these things we are more than conquerors through him who loved us. For I am sure that neither death nor life, nor angels nor rulers, nor things present nor things to come, nor powers, nor height nor depth, nor anything else in all creation, will be able to separate us from the love of God in Christ Jesus our Lord.”
Romans 8:35–39

_{John 6:37–40; John 5:24; Romans 8:1; Ephesians 1:13–14; Philippians 1:6; 1 Peter 1:3–5}