Puts on the Calvinist cap
So, by default he knew those for whom he would die?
Responding as an Arminian: You could say that. I might nit-pick the word "default" there but, essentially, yes.
Switches the Calvinist for an Arminian cap
For the same reason, he predestined us with free will.
Responding as a Calvinist: I cannot decipher how that answers my question. Are you saying, "Because otherwise the free offer of the gospel is not genuine"? If so, I would raise two objections:
(1) The gospel is a royal proclamation (by definition), not a contingency offer. It is announced as an accomplished fact and pressed upon all hearers as an unconditional command (to repent and believe). Salvation is not a suspended transaction awaiting human activation.
(2) The message of the gospel is genuine because it is tied to the truthfulness of the message: In good faith, God commands every human being to repent and promises that every penitent believer will certainly be saved. That statement is true regardless of how many respond because it doesn't imply an intent by God to save each individual; it asserts a plainly conditional promise. A parent can sincerely say to all children at the table, "Anyone who finishes the vegetables may have dessert," without implying any intention by the parent to guarantee that every child will eat the vegetables.
---
gospel (noun): Good news (εὐαγγέλιον), the announced accomplishment of God's saving act in Christ. The gospel is not an
invitation awaiting acceptance, it is the definitive
proclamation that God has fulfilled his redemptive promises in the crucified and risen Christ Jesus, summoning all peoples to repentance and faith.