Studying ancient history is a practice in source criticism, but this truism holds even more than usual when it comes to Alexander. Aside from a smattering of inscriptions and appearances in places like the Babylonian Chronicle, there are five main narrative accounts of Alexander's reign.

1. Diodorus Siculus: 17th book (out of 40) of a universal history written by a Greek from Sicily in the first century BCE.
2. Curtius Rufus: a biography of Alexander in Latin by an educated, perhaps senatorial Roman, probably from the middle of the 1st century CE, but the first two books where he explains who he is and the beginning of the campaign are missing.
3. Plutarch: a biography (as part of the parallel lives) and two ethical treatises written by a 2nd century CE Greek primarily interested in philosophy.
4. Arrian: a history of Alexander's reign long considered the best, written by an upper-class Greek man from Bithynia who served as a Roman consul in the second century. It is unknown whether this is a work of his youth or a mature work. He also wrote an Indica (about Alexander's forces coming back from India) and a now-lost Successors.
5. Justin: a late (maybe late 2nd or 3rd century, maybe later) epitome (synopsis) of the universal history of Pompeius Trogus, who had been Julius Caesar's secretary.

We know that there were many other sources (Arrian explains why you should believe him and not them) and that those histories started soon after Alexander's death. None of the other sources survive.

Broadly speaking, the surviving historians are grouped by which earlier sources they used. Plutarch and Arrian traditionally had a better rep because they followed the histories of Ptolemy and Aristobulus, both men who fought with Alexander, and the others were the vulgate (less reputable) tradition because they followed Cleitarchus who hadn't, though all of the ancient sources had access to additional material that has not survived outside of fragments, most notably Callisthenes, who was Alexander's court historian and propagandist.

And yet, these are the sources we have for knowing anything about Alexander.

In his book The First European, Pierre Briant observed that modern study of ancient historiography largely emerged to try to deal with these issues. One of the questions set in the French academy asked historians to assess which of these sources should be preferentially believed.

So it should be no surprise that these questions, including the attempt to isolate the actual primary material hidden in these ancient secondary sources, are of central importance to modern scholarship on Alexander. The conclusion swings a lot by historian. W.W. Tarn in the early 20th century pushed an Enlightened Alexander, while historians influenced by the Nazi regime saw in Alexander the paranoia, megalomania, and violence of Hitler.

The root of this is an unanswerable question: who is Alexander? The sources and modern historians are obsessed with the man, but our ancient sources are based on other other ancient sources that had their own agendas, including in Alexander's own propaganda. Behind that is a man with a shrouded face onto whom people can project their hopes, fears, and dreams.

With all of that preamble, there are of course a ton of other issues that go into Alexander's conquest, too, including that his father Philip II had gifted him the best professional army money could buy. On this, see Ian Worthington's work who has most aggressively beaten the drum on Philip > Alexander. The way that the sources focus on Alexander ignore most of the issues, including local concerns and collaboration (in Ionia, Egypt, and probably Bactria by the end), they ignore the fighting in places Alexander wasn't, including in Greece, they ignore most of the issues of the governance of where Alexander set up––to name just a few.

The question of Alexander's divinity is tricky. Some of it comes from the prejudices of these later sources that all lived at times where ruler cults were normal. This doesn't mean that they saw the king or emperor as an actual divinity per se, but that there were cults that probably served to unify the territories. Others come from a few episodes in Alexander's reign:

1. Stories about Alexander's divine birth that came after his death (as distinguished from being descended from Gods).
2. An episode in Egypt where the priest at Siwah (mistakenly?) referred to Alexander as "O Pai Dios" (son of god) rather than "O Paidion" (my son). [Corrected to "Paidion," see explanation below]
3. A few "prophecies" of dubious legitimacy (I published on one from Didyma) that were political tools.
4. A demand that the Greek cities establish cults for him.
5. Anecdotes about his increasingly erratic behavior.
6. Adopting Persian court ceremony, including Proskynesis, which required people to kowtow before the king. This is something that Greeks only did before gods, but more likely was an attempt to unify a wildly diverse empire.

There are others, but these are the big ones. If we look at them, most, and perhaps all, have political motivations rather than religious ones. (Much the same happens when looking at the idea that Alexander wanted a brotherhood of mankind––he did, if it resulted in everyone being his loyal subject.) Alexander was a master propagandist, restricting who was allowed to paint or sculpt him and controlling his message back to Greece and he must have been incredibly charismatic. After death, there quickly sprang up numerous cults (more like cults of heroes than cults of personality) for him.

Tl;dr Can we trust the standard narrative of Alexander's reign as told in the surviving sources? No.