I believe this phrase should be translated:
"has in these last days spoken unto us by [his] a son, whom he has appointed heir of all things, by (δι': because of) whom also he made the worlds (ages)."
According to Thayer's Lexicon, δι᾽ means:
"through, on account of, by reason of, for the sake of, because of"
Note that the concordances say δι' means "by, through" when the noun is in the genitive, but it means "because of" in the accusative. I do not believe this is true. Here are a few examples of δι' with a genitive noun:
"By the which will we are sanctified through (because of) the offering of the body of Yeshua Messiah once for all." Hebrews 10:10
"And these all, having obtained a good report through (because of) faith, received not the promise" Hebrews 11:39
"When Yeshua heard that, he said, This sickness is not unto death, but for the glory of Elohim, that the Son of Elohim might be glorified thereby (because of) it." John 11:4
"For Elohim sent not his Son into the world to condemn the world; but that the world through (because of) him might be saved." John 3:17
"Be it known unto you therefore, men and brethren, that through (because of) this man is preached unto you the forgiveness of sins" Acts 13:38
The first two chapters of Hebrews is about mankind. The author is arguing that it wasn't Messengers, or any other divine being, that Elohim made the world for. This is explained in Genesis:
"And Elohim said, Let us make (נַֽעֲשֶׂ֥ה: accomplish; H6213) man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creeps upon the earth." Genesis 1:26
This is why the next verse in Hebrews says:
"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 (δι': because of) himself purged our sins, sat down on the right hand of the Majesty on high; Being made so much better than the Messengers, as he has by inheritance obtained a more excellent name than they."
The author then goes goes on to explain how the Scriptures prove that Elohim has always favored mankind. He ends his prologue in the next chapter with verses 5-18:
"For unto the Messengers has he not put in subjection the world to come, whereof we speak.
But one in a certain place testified, saying, What is man, that you are mindful of him? or the son of man, that you visit him?
you made him a little lower than the Messengers; you crowned him with glory and honor, and did set him over the works of your hands:
you have put all things in subjection under his feet. For in that he put all in subjection under him, he left nothing that is not put under him. But now we see not yet all things put under him.
But we see Yeshua, who was made a little lower than the Messengers for the suffering of death, crowned with glory and honor; that he by the grace of Elohim should taste death for every man.
For it became him, for whom are all things, and by (δι': because of) whom are all things, in bringing many sons to glory, to make the captain of their salvation perfect through sufferings.
For both he that sanctifies and they who are sanctified are all of one: for which cause he is not ashamed to call them brethren,
Saying, I will declare your name to my brethren, in the midst of the church will I sing praise unto thee.
And again, I will put my trust in him. And again, Behold I and the children which Elohim has given me.
Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil;
And deliver them who through fear of death were all their lifetime subject to bondage.
For verily he took not on [him the nature of: italics not in original Greek) Messengers; but he took on [him] the seed of Abraham.
Wherefore in all things it behoved him to be made like unto his brethren, that he might be a merciful and faithful high priest in things pertaining to Elohim, to make reconciliation for the sins of the people.
For in that he himself has suffered being tempted, he is able to succour them that are tempted."
The author never mentions Yeshua until Hebrews 2:9, and notice right before he says "but we see Yeshua", the author says "but now we see not yet all things put under him". This is because the first two chapters are about mankind- all of mankind. Yeshua is a man, and Elohim put all things in subjection to him because this was Elohim's purpose from the beginning.
"Verily, verily, I say unto you, The hour is coming, and now is, when the dead shall hear the voice of the son of Elohim: and they that hear shall live.
For as the Father has life in himself; so has He given to the son to have life in himself;
And has given him authority to execute judgment also, because he is the son of man." John 5:25