Yes, that day of Christ has come and gone.
The better translation is Young's Literal which renders it as "a day of Christ" both times.
"5 for your contribution to the good news from the first day till now,
"6 having been confident of this very thing, that He who did begin in you a good work, will perform [it] till a day of Jesus Christ, .....
*"10 for your proving the things that differ, that ye may be pure and offenceless -- to a day of Christ," (YLT)
The definite article "the" is not in the original Greek. Strong's Gr. 2250 is "ἡμέρα, ας, ἡ", "hemera" and means "a day". Even the Interlinear put it as "the day".
A day of Christ is the same sense and meaning as "the day of the Lord", or "the day of God" (2 Pet. 3:10, 12), and is the same as "a day of their calamity" (Deu. 32:35), or "a day of vengeance" (Prov. 6:24).
It is the same as "the time of the iniquity" (Ezek. 21:25, 29), and as the days of recompense" (Hos. 9:7), or "the time of their visitation" (Jer. 50:27).
A day of the Lord, or the day of God, or a / the day of Christ was a time appointed by God for judgment to be poured out from His throne on high. There have been many of them. We can count a few.
The flood of Noah's day was a day / time of judgment. The burning of Sodom and Gomorrah was another time of judgment. The plagues poured out upon Egypt were times of judgment. Taking the ten northern tribes into Assyria, and the two southern tribes of Judah into Babylonian captivity were days of judgment, days of the Lord. The judgment upon Babylon was "a day of the Lord" (Isa. 13: 6, 9).
The same day that Paul called a day of Christ was stated by Peter as "the day of the Lord" (2. Pet. 3:10) and two verses later he called it "the day of God".
They both were referring to the time of judgment that was about to be poured out upon Jerusalem and all Judea for crucifying Christ. That judgment day has already come and gone. It happened at the destruction of Jerusalem and that temple (which had become profane after His sacrifice) by the Romans in AD 70. God did not wait 2,000+ years to dispense that judgment.
That does not mean that there have not been other days of judgment since then. Christ rules at the right hand of the Father. That means He is sitting on His throne and that means that He is continually judging the nations, and the people.
The OT shows the methods and agents God used to dispense His judgments. He used "fire" from heaven in Sodom and Gomorrah. He used the waters in the flood of Noah. But he also used foreign armies (Assyrians, Medes & Persians, Greeks, Romans, Babylonians). He used droughts and locusts and pestilence (disease) and famines.
All of these were His rods and messengers (Isa. 10:24; Rev. 2:7). They were his strong arm (Psa. 89:10) and hand (Isa. 40:10). They were referred to as "coming in the clouds" for the imagery of God and His son traveling from heaven to earth in the clouds (Job 22:14; Psa. 104:3; Dan. 7:13).
The Jews knew this language. That is why Caiaphas became so angry in Matt. 26 when questioning Christ. He knew Christ had just pronounced judgment upon him when Jesus said in Matt. 26:64,
"...Hereafter shall ye see the Son of man sitting on the right hand of power, and coming in the clouds of heaven." (KJV)
Caiaphas illegally tore his clothes (high priests were never to do that), and proclaimed Christ to have blasphemed because Caiaphas did not recognize Jesus as the Son of God, and believed that Jesus had presumed to pass judgment in place of God. That is why he sent Jesus to be killed.
But, Jesus' judgment upon Caiaphas was a direct judgment, and it was referencing the same day of judgment, the same day of Christ, the same day of God that both Paul and Peter warned of in Philippians and 2 Peter. (See also Acts 2:20, 1 Cor. 1:8; 5:5; 2 Cor. 1:14; 1 Thess. 5:2).
I have actually heard preachers and elders state from the pulpit that Paul, a man filled with the Holy Spirit, one whom Christ appointed (Acts 9:3-18), must have been mistaken. Such arrogance that when scriptures can be questioned as mistaken because they counter our beliefs? Should we proclaim the scriptures in error, or should we begin to reexamine what we think we know?
We are not told of every day / time that God has poured out His judgment upon the people or nations. The Holy Spirit recorded a few of them in the OT. He recorded the one that was coming upon that generation in the NT.
"35 That upon you may come all the righteous blood shed upon the earth, from the blood of righteous Abel unto the blood of Zacharias son of Barachias, whom ye slew between the temple and the altar. 36 Verily I say unto you, All these things shall come upon this generation." (KJV)
A day of judgment was promised to that generation of the first century AD. We cannot presume that it was the only day of judgment, or that there would never be another time of judgment ever again.
The very essence of Christ's reign from on high is an everlasting, continual kingdom, a never ending continual priesthood, and a continual rule. Its very nature denotes continuing judgment. He is in control. We only see the natural events surrounding us. Some of those natural events - tsunamis, hurricanes, floods, tornados - or foreign armies could be His judgments today. His providence is still working for those that love the Lord (Rom. 8:28).
See also "The Days of His Visitation" at my blog ShreddingTheVeil here.