Did any Early Church Father interpret Ezekiel 44:2 to be about Mary?

OP: Did any Early Church Father interpret Ezekiel 44:2 to be about Mary?

It sort of matters what "early" and "church father" mean, but the answer is yes, some did.

From John of Damascus, writing this about 750 AD.

But just as He who was conceived kept her who conceived still virgin, in like manner also He who was born preserved her virginity intact, only passing through her and keeping her closed2460. The conception, indeed, was through the sense of hearing, but the birth through the usual path by which children come, although some tell tales of His birth through the side of the Mother of God. For it was not impossible for Him to have come by this gate, without injuring her seal in anyway. Exposition of the Orthodox Faith Book IV Chapter XIV emphasis mine

The question is from where came this orthodox faith idea that Christ was born from the eastern gate of Ezekiel's temple vision, the side of Mary, rather than from the normal "southern gate"?

To answer we turn to the earlier church father who wrote the Infancy Gospel of James.

This book tells us precisely about the eastern gate.

And immediately the cloud disappeared out of the cave, and a great light shone in the cave, so that the eyes could not bear it. And in a little that light gradually decreased, until the infant appeared, and went and took the breast from His mother Mary. And the midwife cried out, and said: This is a great day to me, because I have seen this strange sight. And the midwife went forth out of the cave, and Salome met her. And she said to her: Salome, Salome, I have a strange sight to relate to thee: a virgin has brought forth -- a thing which her nature admits not of. Infancy Gospel of James Chapter 19

The infant simply appears. The gate is closed. Mary remains in the birth state. In turn this caused Clement of Alexandria on the other side of faith to lament this way.

But, as appears, many even down to our own time regard Mary, on account of the birth of her child, as having been in the puerperal state, although she was not. For some say that, after she brought forth, she was found, when examined, to be a virgin. Stromata Book VII Chapter XVI

For Tertullian, the belief in the ever-virgin idea was promoted by the heretic Marcion. Now whether Marcion used Eze 44:2 to prove his point, we are not told directly, but the links in the side-gate belief from the Infancy Gospel support it.

Therefore if He is to be considered in the flesh,3249 because He was born; and born, because He is in the flesh, and because He is no phantom,—it follows that He must be acknowledged as Himself the very Christ of the Creator, who was by the Creator’s prophets foretold as about to come in the flesh, and by the process of human birth. Against Marcion Book III Chapter XI

Nonetheless, the Ezekiel reference continues with Jerome.

The Prophet Ezekiel too had predicted the miraculous manner of that birth, calling Mary figuratively “the Gate of the Lord,” the gate, namely, through which the Lord entered the world. For he saith, “The gate which looks towards the East shall be closed, and shall not be opened, and no one shall pass through it, because the Lord God of Israel shall pass through it, and it shall be closed.”3279 What could be said with such evident reference to the inviolate preservation of the Virgin’s condition? Commentary on Apostles Creed Section 9

So, did early church fathers suggest Ezekiel 44:2 was about Mary? Yes some did, it is clearly implied based on the Infancy Gospel and a desire to preserve Mary's honor. 300 years later the linkage is clearly enumerated by later church fathers.

Keep in mind, the early church fathers tended to focus on fighting the heresies of their day. They didn't write much about Mary's perpetual virginity (and thus link Ezekiel 44:2 to Mary) until the Antidicomarianites showed up and started challenging that around the 3rd century.

That said, here's the historical commentaries on this verse (from Historical Christian Faith Commentaries):

[AD 397] Ambrose of Milan: Who is this gate, if not Mary? Is it not closed because she is a virgin? Mary is the gate through which Christ entered this world, when He was brought forth in the virginal birth and the manner of His birth did not break the seals of virginity. - The Consecration of a Virgin and the Perpetual Virginity of Mary, 8:52

[AD 411] Tyrannius Rufinus: The words of the Prophets concerning Him, "A Virgin shall conceive and bring forth a Son," are known to all, and are cited in the Gospels again and again. The Prophet Ezekiel too had predicted the miraculous manner of that birth, calling Mary figuratively "the Gate of the Lord," the gate, namely, through which the Lord entered the world. For he says, "The gate which looks towards the East shall be closed, and shall not be opened, and no one shall pass through it, because the Lord God of Israel shall pass through it, and it shall be closed." What could be said with such evident reference to the inviolate preservation of the Virgin's condition? That Gate of Virginity was closed; through it the Lord God of Israel entered; through it He came forth from the Virgin's womb into this world; and the Virgin-state being preserved inviolate, the gate of the Virgin remained closed forever. Therefore the Holy Ghost is spoken of as the Creator of the Lord's flesh and of His temple. - Commentary on the Apostles' Creed, Section 9

[AD 420] Jerome Some quite emphatically understand this closed gate through which only the Lord God of Israel passes... as the Virgin Mary, who remains a Virgin before and after childbirth. In fact, she remains always a Virgin, in the moment in which the Angel speaks with her and when the Son of God is born. - Commentarium in Evangelium Lucae, PL 25, 430.

[AD 430] Augustine of Hippo (as quoted by Aquinas) What means this closed gate in the House of the Lord, except that Mary is to be ever inviolate? What does it mean that 'no man shall pass through it,' save that Joseph shall not know her? And what is this - 'The Lord alone enters in and goeth out by it' - except that the Holy Ghost shall impregnate her, and that the Lord of angels shall be born of her? And what means this—'it shall be shut for evermore' - but that Mary is a virgin before His Birth, a virgin in His Birth, and a virgin after His Birth? - De Annunt. Dom. iii

[AD 458] Theodoret of Cyrus It is very likely that these words refer to the womb of the Virgin, through which no one enters and from which no one departs other than the only one who is the Lord. - Commentary on Ezekiel 16.44

[AD 749] John Damascene But just as He who was conceived kept her who conceived still virgin, in like manner also He who was born preserved her virginity intact, only passing through her and keeping her closed. [Ezekiel 44:2] The conception, indeed, was through the sense of hearing, but the birth through the usual path by which children come, although some tell tales of His birth through the side of the Mother of God. For it was not impossible for Him to have come by this gate, without injuring her seal in anyway. The ever-virgin One thus remains even after the birth still virgin, having never at any time up till death consorted with a man. - An Exposition of the Orthodox Faith (Book IV), Chapter 14

[AD 1274] Thomas Aquinas On the contrary, It is written (Ezekiel 44:2): "This gate shall be shut, it shall not be opened, and no man shall pass through it; because the Lord the God of Israel hath entered in by it." Expounding these words, Augustine says in a sermon (De Annunt. Dom. iii): "What means this closed gate in the House of the Lord, except that Mary is to be ever inviolate? What does it mean that 'no man shall pass through it,' save that Joseph shall not know her? And what is this—'The Lord alone enters in and goeth out by it'—except that the Holy Ghost shall impregnate her, and that the Lord of angels shall be born of her? And what means this—'it shall be shut for evermore'—but that Mary is a virgin before His Birth, a virgin in His Birth, and a virgin after His Birth?" - Summa Theologiae, Third Part, Question 28, Article 3