Does the Bible teach there was a time before time? Yes and no. Lets look at a couple of translations. The first is the King James and the second is the New King James translation.
2Ti 1:8 KJV
Be not thou therefore ashamed of the testimony of our Lord, nor of me his prisoner: but be thou partaker of the afflictions of the gospel according to the power of God;
2Ti 1:9
Who hath saved us, and called
us with an holy calling, not according to our works, but according to his own purpose and grace, which was given us in Christ Jesus
before the world began,
2Ti 1:8 NKJV
Therefore do not be ashamed of the testimony of our Lord, nor of me His prisoner, but share with me in the sufferings for the gospel according to the power of God,
2Ti 1:9
who has saved us and called
us with a holy calling, not according to our works, but according to His own purpose and grace which was given to us in Christ Jesus
before time began,
Both translations are not exactly correct. I think the KJV has the right concept but its not a woodenly literal translation. The Greek word that may be translated "world" is kosmos (κόσμος). The Greek word that may be translated "time" is chronos (χρόνος). Here in the original, the word chronos is used. So why did the KJV translate it world? I think they looked at the context and the original Greek and realized Paul meant before a certain "age time". In the English translation you don't see the word "age" that may be translated from
aiōnios (αἰώνιος)
I have bolded chronos (time) and aiōnios (age) in the original below. The tenses change the word slightly but you can still spot them.
1:9 τοῦ σώσαντος ἡμᾶς καὶ καλέσαντος κλήσει ἁγίᾳ οὐ κατὰ τὰ ἔργα ἡμῶν ἀλλὰ κατὰ ἰδίαν πρόθεσιν καὶ χάριν τὴν δοθεῖσαν ἡμῖν ἐν Χριστῷ Ἰησοῦ πρὸ
χρόνων αἰωνίων
So here's a fair translation.
2 Ti 1:9 God, has saved us and called us with a holy calling, not according to our works, but according to His own purpose and grace which was given to us in Christ Jesus before age times.
Therefore the KJV has the right concept and the NKJV is more literal but both leave out the word "age".
There are other verses that are used to prove there was a time before time but you have to ask. Were these passages translated with Pagan Greek philosophy in mind when they were translated "before time began"? I think so.
We can get into a discussion about free will vs no free will when it comes to foreknowledge but the point is this, time is just the distance between events and the future does not exist. However I think the bigger question is, who or what is to blame for the brokenness of this world?