Are you sure that God wants everyone to be saved?
There are many Christian philosophers who do indeed claim that this is the case, but it seems to me that this concept contradicts scripture.
John 12:39-40 (re Isaiah 6:8-10)
For this reason they could not believe, for Isaiah said again, "HE HAS BLINDED THEIR EYES AND HE HARDENED THEIR HEART, SO THAT THEY WOULD NOT SEE WITH THEIR EYES AND PERCEIVE WITH THEIR HEART, AND BE CONVERTED AND I HEAL THEM."
It would seem from this passage of scripture that God is going out of His way to prevent people from being saved.
The Apostle Paul further describes God's blinding and heart-hardening work among Paul's people, the Jews, to prevent many of them from being saved, in the Book of Romans:
Romans 11:8-10 & 25
...just as it is written, "GOD GAVE THEM A SPIRIT OF STUPOR, EYES TO SEE NOT AND EARS TO HEAR NOT, DOWN TO THIS VERY DAY." And David says, "LET THEIR TABLE BECOME A SNARE AND A TRAP, AND A STUMBLING BLOCK AND A RETRIBUTION TO THEM. LET THEIR EYES BE DARKENED TO SEE NOT, AND BEND THEIR BACKS FOREVER."... For I do not want you, brethren, to be uninformed of this mystery -- so that you will not be wise in your own estimation -- that a partial hardening has happened to Israel until the fullness of the Gentiles has come in.
Paul also tells us that God decides who He will save and who He will not. His mercy is bestowed as He Himself sees fit, and upon others He chooses to demonstrate His power and wrath:
For He says to Moses, "I WILL HAVE MERCY ON WHOM I HAVE MERCY, AND I WILL HAVE COMPASSION ON WHOM I HAVE COMPASSION." So then it does not depend on the man who wills or the man who runs, but on God who has mercy. For the Scripture says to Pharaoh, "FOR THIS VERY PURPOSE I RAISED YOU UP, TO DEMONSTRATE MY POWER IN YOU, AND THAT MY NAME MIGHT BE PROCLAIMED THROUGHOUT THE WHOLE EARTH." So then He has mercy on whom He desires, and He hardens whom He desires. You will say to me then, "Why does He still find fault? For who resists His will?"
The Apostle compares God to a potter, and us to His clay. The point behind this comparison is that the potter has complete and total authority over the clay, and if the potter makes one pot for honor, and another for some kind of base use, that is His prerogative. The clay becomes whatever the potter chooses to make it.
Perhaps a good comparison for us today would be someone skilled with ceramics. The ceramic worker may create a beautiful and delicate doll, or an ornate plate to be hung on the wall, or a toilet. All of those things may be "good" as far as the worker is concerned, and the ceramic material would have no justification to complain about being made into a toilet instead of a doll.
The Bible seems to say that when one of us becomes the equivalent of a toilet, it is because that was God's design to begin with.
Or does not the potter have a right over the clay, to make from the same lump one vessel for honorable use and another for common use? What if God, although willing to demonstrate His wrath and to make His power known, endured with much patience vessels of wrath prepared for destruction? And He did so to make known the riches of His glory upon vessels of mercy, which He prepared beforehand for glory, even us, whom He also called, not from among Jews only, but also from among Gentiles.
Thus, the idea that God wants everyone to be saved doesn't seem to be a Biblical viewpoint. Having said that, there are several scriptures that need to be explained in this context.
2 Peter 3:9
The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.
This verse clearly says that God does not want anyone to perish, but rather wants everyone to repent, doesn't it?
When read in context, it seems clear that that is not in fact what the verse says. The main subject of Peter's statements is the amount of time that will pass before the end of the world. Peter informs us that the day of destruction and judgment of ungodly men will indeed come, however, not all of the elect have yet come to Christ. If the Lord were to bring the end of the world now, many who are elect would be condemned with the reprobate and unrepentant, since these particular elect have not yet repented. God is not willing that any of the elect should perish with the ungodly, but rather that all of the elect should come to repentance, and He has not caused them to yet. They each will at their own appointed time. This is why God has not yet brought about the end of the world -- He doesn't want to destroy any of the elect with the ungodly.
1 Timothy 2:3-4
This is good and acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth.
Doesn't this verse clearly say that God desires all men to be saved?
Again, pulled out of context, that does appear to be what it says. However, in context, the meaning of this passage could easily be taken to mean that God desires men of all types to be saved, namely, kings and those in authority as well as common folk, and perhaps also Gentiles as well as Jews (a common theme throughout the New Testament). God is not only interested in saving one class of people, but rather people from all classes.
"For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life. For God did not send the Son into the world to judge the world, but that the world might be saved through Him."
Certainly, Christ is here saying that God wants the whole world to be saved, right?
Maybe not. Here's a passage also talking about the world being saved that may shed some light on the meaning of John 3.
2 Corinthians 5:18-19
Now all these things are from God, who reconciled us to Himself through Christ and gave us the ministry of reconciliation, namely, that God was in Christ reconciling the world to Himself, not counting their trespasses against them, and He has committed to us the word of reconciliation.
All Christians are Particularists as opposed to Universalists -- specifically, we believe that only particular people will go to heaven and not everyone universally. Only some will be saved. John 3:16 says that those who believe will be saved. 2 Corinthians 5:19 says that God was reconciling the world to Himself. Those who are reconciled to God are "the world" according to Corinthians, and according to John, this same group consists entirely of they who believe.
In other words, Christ did not come because God wanted every human in the entire world to be saved, but rather, Christ came because God wanted believers throughout the world (and the whole world of believers) to be saved, namely, God's elect.
Blessed be the God and Father of our Lord Jesus Christ, who has blessed us with every spiritual blessing in the heavenly places in Christ, just as He chose us in Him before the foundation of the world, that we would be holy and blameless before Him. In love He predestined us to adoption as sons through Jesus Christ to Himself, according to the kind intention of His will, to the praise of the glory of His grace, which He freely bestowed on us in the Beloved.
Going back to the original question, why did God provide salvation in the specific way that He did, there are many things God "could" have done differently from our perspective. However, God is necessarily perfect, and all that He does is necessarily best. Logic insists upon it (for there could be no "best" if it were not defined by the character of God), and scripture likewise proclaims it (Isaiah 25:1; Matthew 5:48; Mark 10:18). He chose according to His perfect knowledge the perfect time for Christ (Galatians 4:4), and He also chose according to His perfect wisdom who would believe and who would not.
Absolutely nothing happens apart from His will (Psalm 115:3; Psalm 135:6; Matthew 10:29), and His will is always best by definition.