There really is no question that Mark is the first to write a Greek gospel. The Markan content in the Gospels of Matthew and Luke are both correcting Mark's Greek grammar and making some small factual revisions that add precision to the text. The reason Matthew's gospel would still be first is that he wrote the first gospel-like documents in Aramaic. What we have in our current Bibles is his revised, much longer work in Greek that includes within it Mark's work.

The hypothesis of the 'Q' document to account for the differences between Matthew and Luke is an invention of source criticism - the same field that gave us and perpetuates the Documentary Hypothesis. It stands and falls under many of the same criticisms. Even though no 'Q' document has been found and the early Church Fathers such as Jerome do not mention such a document, there are witnesses to early documents in general, and it is reasonable to assume there were other documents that the Gospels drew upon. There is no reason to assume that all of the content came straight from an oral tradition.

The Synoptic Problem by Daniel B. Wallace - bible.org

The Synoptic Problem is easily solved if we have several written sources the synoptic authors could draw from. The source of those documents would be some mixture of the inner circle of apostles, close peripheral followers, and notes from literate hearers of Jesus - like bootleg recordings at a concert. The writer of the Gospel of Luke insinuates that he drew from several sources like this. It is possible there were even documents from the "scribes and Pharisees" surveilling Jesus to determine his motives and risk for the Sanhedrin. Many of these texts and oral traditions could have been combined and abridged into one Q-like document, but again, a single document doesn't actually solve the Synoptic Problem.

Going through the Gospels, it is not always clear what the inner circle of twelve disciples do. It was not Jesus and the twelve couch potatoes! They each had responsibilities and jobs that served the group. Matthew's career before becoming a disciple was that of a tax collector, a literate profession that required skills in accounting and long-term record keeping. He naturally would fit into the roles of either being the treasurer - a role which the gospels tell us goes to Judas - or recording the events and sayings of Jesus and the apostles. Matthew might even have been Jesus' personal secretary.

This puts Matthew in the position of creating a collection of speeches, stories and maybe 'Q' like documents of sayings. Copies could have gone to each of the apostles, established congregations and other entrusted believers such as Paul. An abridged version might have been distributed even more widely. The nature of the Synoptic problem is such that it is doubtful that there is one single 'Q' like document that accounts for the gospels or even the differences between Matthew and Luke.

One witness confirms this role for Matthew. Writing prior to 109 AD, Papias of Hieropolis is quoted by Eusebius as saying:

So then Matthew wrote the oracles in the Hebrew language, and every one interpreted them as he was able. - Eusebius, NPNF2-01 - ccel.org 

Papias seems to be insinuating that people were having difficulty reading "Hebrew" (ie. Aramaic). Frank observations and minor criticisms like this add credibility to the source. Papias also relates concerning Mark, openly questioning the sequence of events in Mark's gospel:

This also the presbyter [John] said: Mark, having become the interpreter of Peter, wrote down accurately, though not in order, whatsoever he remembered of the things said or done by Christ. For he neither heard the Lord nor followed him, but afterward, as I said, he followed Peter, who adapted his teaching to the needs of his hearers, but with no intention of giving a connected account of the Lord’s discourses, so that Mark committed no error while he thus wrote some things as he remembered them. For he was careful of one thing, not to omit any of the things which he had heard, and not to state any of them falsely. - Eusebius, NPNF2-01 - ccel.org 

Connecting the dots, the apostle Matthew produced several documents in Aramaic (or closely related Hebrew) which may have included a Q-like sayings document and/or a gospel. Of the gospels we have, Mark was the first to Greek and his work was sourced from the apostle Peter combined with whatever materials he had from Matthew and others. 

It is apparent and entirely conceivable that Matthew took Mark's Gospel, refined and corrected the Greek, and added in some other choice material. Since Matthew was an authority himself and seeing elements of his work in Mark's Greek manuscript, there would be no concern of plagiarism or cooption. Because 97% of the Gospel of Mark is within Matthew's Gospel, the retaining of both Gospel's as canonical by the early churches would demonstrate the agreement between Peter and Matthew, a matter of some importance as the last chapter of the Gospel of John suggests (Wallace 2004)

The power of the Peter-Mathew agreement doesn't entirely diminish if it was a protégé of Matthew who revised Mark's Gospel and added translations of some of Matthew's documents to the text. There is a telling reason to believe this is the minimum connection to Matthew - why wouldn't a Q-like sayings document be available if Mark's Gospel was not just available but canonized? Repetition wouldn't be a concern unless the Gospel of Matthew superseded a Q document written by Matthew or there wasn't a specific Q document to begin with.

As Asimov states, the genealogy of Joseph must go through David to be the Messiah, but there are at least three problems with this genealogy.

1. Asimov relates how Matthew's nice clean summary of 3 sets of 14 generations leading to Jesus is cherry picking - the second set of 14 should actually be at least 18. Why are at least four documented generations missing from the genealogy? Furthermore, when matching generations to chronology it becomes clear there must be other missing generations.

2. In the third set of "fourteen generations," there are only 13 generations by normal counting. Why?

3. A problem that Asimov does not reference is the Curse of Jeconiah. In Jeremiah 22:24-30

Asimov unwittingly comes close to dealing with each of these problems in turn, but then comes to the wrong conclusions. The short answer to all three of these problems is that Matthew's generations are only of the Deemed and Redeemed. He excludes the unrepentant.

As noted in the AGB, this genealogy is odd for including a number of women. 

1 Chronicles 2:51

Zerubabel - in the direct line of Davidic Kings - was the governor of Jerusalem during the building of the second temple. 

The Problem of the Curse on Jeconiah in Relation to the Genealogy of Jesus - jewsforjesus.org

Biologically, Jesus is not a descendant of Jeconiah. Joseph's importance is what he provides in terms of inheritance by law. He is of the kingly line of David. Jesus by law inherits that line. Though Jeconiah has been forgiven and redeemed, technically the original curse has stood. 

Regardless of whichever way the wind blows concerning the chronology of Herod the Great, the astronomy of the star the wise men followed should be located in one of two particularly rare sets of events. 

1. Two extremely close conjunctions of Venus and Jupiter - the two brightest objects in the night sky after the moon. Each conjunction was so close that they looked like one extremely bright star. In between and surrounding these conjunctions are other astrologically significant events. The combination of both of these conjunctions correlates more specifically with the events in Matthew's text than any other known astronomical events.

2. A long period comet appearing first as a growing fetus inside the constellation Virgo as the comet travels towards the sun. The comet's movement makes it appear that Virgo is giving birth before it is washed-out in the light of the sun. It appears again leaving the sun literally pointing to a house in Bethlehem.