First, I would have to argue that all the gospels present Yeshua as a man, because I believe he is a man. But one thing that I find particularly relevant about Luke's gospel is his account of Yeshua after his resurrection.
"And as they thus spake, Jesus himself stood in the midst of them, and saith unto them, Peace be unto you.
But they were terrified and affrighted, and supposed that they had seen a spirit.
And he said unto them, Why are ye troubled? and why do thoughts arise in your hearts?
Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have.
And when he had thus spoken, he shewed them his hands and his feet.
And while they yet believed not for joy, and wondered, he said unto them, Have ye here any meat?
And they gave him a piece of a broiled fish, and of an honeycomb.
And he took it, and did eat before them." Luke 24:36-43
This shows us that the resurrected Messiah was a human, rather than some spiritual entity floating around like a particle of light.
As far as conservative Christianity goes, the earliest I can find is from John Nelson Darby, the man who made up the "pre-tribulation rapture". The article says:
In the Gospel of Luke, the Lord Jesus is specially brought before us as the Son of man. It has been often remarked the contrast there is between John's Gospel and Matthew's...
...In Luke's Gospel there is what might at first appear a difficulty to the mind, but it brings out Christ in a special way, so I speak of it here. In Luke there is more suffering in Gethsemane than in any other Gospel; and on the cross none at all. Why is this? Because, as man, He is above all that He is passing through. The character of the Lord's sufferings in Luke would lead us to remember, for the precious comfort of our souls, that He was perfect Man - sinless, of course, but a Man. When risen, He says, "Behold my hands and my feet that it is I myself; handle me and see, for a spirit hath not flesh and bones as ye see me have." (24:39) He would bring home to the soul all the blessed truth of how thoroughly He was Man. Look how that is marked in Gethsemane: "When he was at the place, he said unto them, Pray that ye enter not into temptation." (22:40) In Luke you find Him constantly praying as man - perfect man, obedient and dependent. "Man shall not live by bread alone, but by every word that proceedeth out of the mouth of God." (Matt 4:4) In Luke we find Him "all night in prayer to God." (6:12) At another time "He went up into a mountain to pray, and as he prayed the fashion of his countenance was altered," and He was transfigured. (9:28) In Gethsemane, "He kneeled down and prayed, saying, Father, if thou be willing, remove this cup from me; nevertheless, not my will but thine be done. And there appeared an angel unto him from heaven strengthening him, and being in an agony he prayed more earnestly." There you get the Man again.
Also, a man named Ray Stedman has an article called Luke: The Perfect Man. His basis for this is:
"The Son of man is come to seek and to save that which is lost" Luke 19:10
John Darby is a very famous theologian, so as far as I can tell, the phrase "the Gospel of Luke presents Jesus as the Son of Man" originated with him.