② predetermination, of God’s omniscient wisdom and intention (so Alex. Aphr., Fat. 30 p. 200, 31 Br.; Proverbia Aesopi 131 P.; Jdth 9:6; Just., D. 92, 5 πρόγνωσιν ἔχων) w. βουλή Ac 2:23. κατὰ πρόγνωσιν θεοῦ πατρός destined by God the Father (NRSV) 1 Pt 1:2 (Just., D. 134, 4; s. WArndt, CTM 9, 1929, 41–43).—DELG s.v. γιγνώσκω. M-M. TW.
Arndt, W., Danker, F. W., & Bauer, W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 867). Chicago: University of Chicago Press.
The answer to your question hinges on the definition of πρόγνωσις.
According to BDAG the proper translation is predetermination.
Here is the same word used within context from the LXX (english translated)
5 “For you have done these things and those that went before and those that followed. You have designed the things that are now, and those that are to come. What you had in mind has happened; 6 the things you decided on presented themselves and said, ‘Here we are!’ For all your ways are prepared in advance, and your judgment is with foreknowledge.
The Holy Bible: New Revised Standard Version. (1989). (Jdt 9:5–6). Nashville: Thomas Nelson Publishers.
TDNT has this to say (amongst a whole lot more):
The corresponding use for knowledge on God’s part in the sense of election, which is so characteristic of the OT, is occasionally found, most dearly at 2 Tm. 2:19: ἔγνω κύριος τοὺς ὄντας αὐτους (== Nu. 16:5; cf. also Mt. 7:23), but also 1 C. 8:3; 13:12; Gl. 4:9 (→ infra). This usage is the furthest from ordinary Greek and was later abandoned.
Kittel, G., Bromiley, G. W., & Friedrich, G. (Eds.). (1964–). Theological dictionary of the New Testament (electronic ed., Vol. 1, p. 706). Grand Rapids, MI: Eerdmans.
This gives a little insight:
Peter elaborated on the descriptive term “God’s elect” (cf. 2:9) who have been chosen according to the foreknowledge of God. God’s choice is part of His predetermined plan, and is not based on any merit in those who are elected, but solely on His grace and love for them before their creation.
As the Williams translation puts it, God’s choosing is “in accordance with” (kata) or in keeping with His foreknowledge. This seems preferable to the view that election follows or is based on foreknowledge. Moreover the word for foreknowledge (prognōsin) means more than a passive foresight; it contains the idea of “having regard for” or “centering one’s attention on” (cf. Kenneth S. Wuest, First Peter in the Greek New Testament for the English Reader, p. 15). The same word is used in 1:20 of Christ who was “chosen” by the Father before Creation. The Father did more than merely know about His Son ahead of time; He knew Him completely. Thus God chose all those on whom He focused His attention (by His grace, not because of their merit).
Raymer, R. M. (1985). 1 Peter. In J. F. Walvoord & R. B. Zuck (Eds.), The Bible Knowledge Commentary: An Exposition of the Scriptures (Vol. 2, p. 840). Wheaton, IL: Victor Books.
Similar is this verse:
23 this Man, delivered over by the predetermined plan and foreknowledge of God, you nailed to a cross by the hands of godless men and put Him to death.
New American Standard Bible: 1995 update. (1995). (Ac 2:23). LaHabra, CA: The Lockman Foundation.