"1God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,
2 Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds;
3 Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high:" (KJV)
The book of Hebrews is generally thought to have been written about AD 60 to 65. The demonstrative "these" is key. Verse 1 tells us that at various times prior to (in the past) the Father had spoken to the people in various ways through the prophets. The word went from the Father to the prophets, and then the prophets spoke directly to the people.
When did Christ speak directly to the people? We know that He was manifested on earth in the 1st century A.D., and we know that Heb. 1:2 says He spoke to them in "these last days", therefore the time of His speaking were the last days. A = B = C. Christ spoke to the people in the 1st century A.D., and Christ spoke to the people in "these last days", so the 1st century A.D. equals "these last days".
The demonstrative "these" belongs to the time the words were written! They do not refer to the the time, or days in which we are reading them.
Vs. 3 says that when Christ purged our sins, He then sat down on the right hand of the Father... the Majesty on high. We don't seem to have any problem understanding that He purged our sins when He died on the cross in our place, and that within days of His crucifixion is when He ascended to the Father (Acts 1:9) in that generation of the first century A.D.
The time period is the same. He spoke to them in those days of the 1st century A.D., and he ascended to the Father in those same days!
The problem is people's ideas... their presumptions, their biases, their taught perspective... on what the "last days" were. People want to assume the last days or end times is about the end of the physical cosmos / world. That is wrong, as the Bible never speaks about the end of the physical world, or the end of Christ's kingdom. His kingdom is everlasting, world without end (Isa. 45:17; Eph. 3:21).
Hebrews tells us what was ending, what was ready to pass away when the book was written. It was the old covenant, and the sacrificial Mosaic temple that was coming to an end.
"In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away." (KJV)
The new covenant was going to replace the old covenant in those last days of that Mosaic sacrificial temple. Christ's sin offering on that cross at Golgatha took the place of all the old sacrificial law that had been given by Moses to the children of Israel. Christ, a prophet like Moses, went to that cross once forever, once for all as the lamb slain from the foundation of the world (Heb. 7:27; 9:12. 26; 10:10-12) .
Matt. 10:23, where Christ was giving specific instructions to the twelve disciples of what they should say, and how they should go to the lost sheep of Israel,
"But when they persecute you in this city, flee ye into another: for verily I say unto you, Ye shall not have gone over the cities of Israel, till the Son of man be come."
He told His disciples that some of them would not finish before He came back to them.
"33 Ye serpents, ye generation of vipers, how can ye escape the damnation of hell?
34 Wherefore, behold, I send unto you prophets, and wise men, and scribes: and some of them ye shall kill and crucify; and some of them shall ye scourge in your synagogues, and persecute them from city to city:
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."
"This generation" is not our generation, nor any other generation than the one in which Christ spoke directly to the scribes and Pharisees. They were going to receive the judgment of all of the righteous bled shed from Abel to Zacharias, and many of them lived to see it happen.
1 Pet. 1:19-20,
" But with the precious blood of Christ, as of a lamb without blemish and without spot: 20 Who verily was foreordained before the foundation of the world, but was manifest in these last times for you,"
The last times, the last days was when Christ was manifested, and appeared to the people on this earth.
Jacob prophesied of those days when giving the blessings to his sons on his death bed in Gen. 49:1-27. Gen. 49:1,
"And Jacob called unto his sons, and said, Gather yourselves together, that I may tell you that which shall befall you in the last days."
Jacob was speaking to his sons. The last days concerned the last days of the tribes of Israel. And, notice what Jacob said in verse 10:
"The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be."
The scepter passed from Judah to Christ when He died on the cross, and then ascended to our Father in heaven in the first century A.D. And, notice the next two verses:
11 Binding his foal unto the vine, and his ass's colt unto the choice vine; he washed his garments in wine, and his clothes in the blood of grapes:
12 His eyes shall be red with wine, and his teeth white with milk."
Washing his garments in the wine, in the "blood of the grapes" is a clear reference to the winepress of the battle in Revelation (Rev. 14:19-20; 19:15).
The link of the last days of the tribes of Israel to the cross of Christ, to the coming of His kingdom, to the judgment to fall upon that generation, is clear throughout all of the Bible to be the first century A.D. and the final destruction of Jerusalem and that old Mosaic sacrificial temple in A.D. 70.
There is much more that can be shown, and is evidenced through the scriptures the "last days" were those days of the first century A.D. I recommend my posts "Daniel and The End Times", "Did Christ Lie To His Disciples", all 10 parts of "It's Not The End of The World", "The Latter Days Are Not Our Days", and many more at my blog ShreddingTheVeil.
All sources are from the KJV. All bold emphasis is mine.