How does the record of Christ's conception and birth allow for the idea that he physically existed beforehand?

I don't believe the Scriptures mean that Jesus Christ literally lived before he was born to Mary, the Gospels don't allow for that. Jesus was foretold as coming because his Father, the LORD God, knew what would be needed to save people from their sins. Jesus was the sinless man who died that we might live, just as his Father intended. For a sinless man could not be held by the bonds of death.

Jesus existed beforehand in a Divine form. He left his throne and all his glory behind to take on the form of a human. Now just because he left his throne and glory behind does not mean he left his Divinity behind. After he died for us all on the cross he took it all up again.

No human (only human)) Jesus was all human and all Divine) can live before they are begotten. We should not look at what happens with us and think that God/Jesus should be like us. Yes we were made in the image of God (character/potential) but God was NOT made in ours.

John 1:1-2 The Word was first, the Word present to God, God present to the Word. The Word was God, in readiness for God from day one.

John 17:5 And now, Father, glorify me in your presence with the glory I had with you before the world began.

Matthew 25:31 "When the Son of Man comes in his glory, and all the angels with him, he will sit on his throne in heavenly glory.

Matthew 23:22 And he who swears by heaven swears by God's throne and by the one who sits on it.

There are other verses where Jesus himself said that he lived in heaven before he came to earth:

Joh 6:38 “. . .because I have come down from heaven to do, not my will, but the will of him that sent me.”

Joh 6:62 “. . .What, therefore, if YOU should behold the Son of man ascending to where he was before?”

Joh 17:4-5 “. . .I have glorified you on the earth, having finished the work you have given me to do. 5 So now you, Father, glorify me alongside yourself with the glory that I had alongside you before the world was.”

And others:

Joh 1:1 “In [the] beginning the Word was, and the Word was with God, and the Word was a god.”

Joh 8:58 “Jesus said to them: “Most truly I say to YOU, Before Abraham came into existence, I have been.””

Col 1:15 “He is the image of the invisible God, the firstborn of all creation;”

You are correct about the begotten part but he was that before he came to earth, it wasn't because of his birth here that made him begotten.

this is how:

In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. (John 1:1-3)

And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth. (John 1:14)

Before being born of Mary, Jesus Christ was not in a physical form, only in a Spirit form - you have answered your own question

Oh snap!