Arius wrote that the Son was “begotten timelessly by the Father … before aeons … begotten timelessly before everything” (Letter to Alexander – See RPC Hanson, The Search, page 8). But Alexander of Alexandria stated that Arius also wrote that “there was a time when he did not exist” (RPC Hanson, The Search, page 16). Did Arius contradict himself? How could there be time before the Son existed if he was “begotten timelessly before everything?”
If your first source is correct (with the missing ellipsis bits not making any difference to the rest), then the quote of Arius a few pages further on surely does show up a contradiction in the man's statements.
However, you have the advantage over others who do not have that book to hand because a study of it might find the author, Hanson, explaining away any apparent contradiction. Or, if he does not, could you just simply state plainly that Hanson does not do that? For sure, there is not nearly enough in the minute quotes from Arius to give us any idea as to what he taught about time existing before the Son existed (or not.)
The same kind of problem arises with Origen's statements on the Logos / Word in no way having been created or begotten in time. Here this scholar notes:
"This is ironic since Arius, the archenemy of the doctrine of the Trinity in the fourth century, claimed Origen as the source of his subordinationism of the Son in which he declared that "there was when the Son was not"." The Story of Christian Theology, pp 109-110, Roger E. Olson, Apollos 1999
Olson then goes on to show how radically different Origen was to Arius. Origen stated the exact opposite to Arius's last quote. Hence the irony of Arius claiming Origen in support. Chaper 9 deals with the differences. Back then, there were some who believed that
"Jesus Christ was the incarnation, not of God, but of a great creature of God, the Logos, who had a beginning in time and remained forever subordinate to the Father, not only in terms of his role but also in terms of his very being." Ibid. p.142
"Indeed, the agreement of the ancients is clearly seen here, that in the Council of Nicaea, Arius dared not make a pretense on the basis of the authority of any proved writer." Ibid. p.158
A further difficulty trying to answer any apparent contradictions of Arius is his reputed record of verbal duplicity. Long before our Politically Correct Era, John Calvin said this about Arius:
"Arius confessed that Christ was God and the Son of God... yet in the meantime he did not cease to prate that Christ was created and had a beginning, as other creatures. The ancients, to drag the man's versatile craftiness out of its hiding places, went further, declaring Christ the eternal Son of the Father, consubstantial with the Father. Here impiety boiled over when the Arians began to hate and curse the word homousious [ft. - consubstantial, the word of emphasis in the Creed of Nicaea, 325, by which Arianism was rejected.]
... If it came to a debate, he was accustomed to confess that he recognized the Father as God, the Son as God, and the Spirit as God, but afterwards a way out was found, contending that he had said nothing else than if he had spoken of God as strong, and just, and wise. And so he re-echoed another old song, that the Father is the Son, and the Holy Spirit the Father, without rank, without distinction. To shatter the man's wickedness the upright doctors, who then had piety at heart, loudly responded that three properties must truly be recognized in the one God. And that they might fortify themselves against his tortuous cunning with the open and simple truth, they truly affirmed that a trinity of persons subsists in the one God, or, what was the same thing, subsists in the unity of God." Calvin : Institutes of the Christian Religion Vol. 1, page 125 ed. by John T. McNeill, Westminster
Whatever Arius taught about time existing before the Son [of God] existed is suspect due to his idea that there was a time when the Son was not. It is that later part of the question that should dictate how to view the first part of the question, though others may disagree. Those who agree with Arius will certainly disagree with my answer but I will not argue or debate with any of them.
Arius, the fourth-century presbyter after which Arianism is named, taught that God created all things through His Son. For example, Athanasius, in his paraphrase of Arius’ writings, wrote:
“When He (God) wanted to make us, He then made a certain Person and called him Word and Spirit and Son so that he could make us” (RH, 13).
If God made all things through His Son, then the Son must have existed before all things. Consistent with this concept, Arius wrote that the Son was:
“begotten timelessly by the Father … before aeons … begotten timelessly before everything” (Letter to Alexander, RH, 8).
However, Arius also frequently said that the Son did not always exist. For example:
The Son “did not exist before he was begotten” (Arius' letter to Eusebius of Nicomedia - RH, 6)
This gives us Arius' famous phrase that was anathematized by the Nicene Creed: “There was when He was not.”
In the very little of Arius’ own writings that survived until today, Arius never said there was “time” before the Son was begotten. But, according to Athanasius and Alexander, Arius did say that. For example:
“There was a time when the Son of God did not exist” (Alexander, RH, 17).
So, did Arius contradict himself? How could Arius say that there was "time" before the Son existed if he was “begotten timelessly before everything” and created all things?
“Gwatkin characterizes Arianism as … a crude and contradictory system” (RW, 10). However, the Trinitarian Bishop Rowan Williams, after a detailed intense study of Arius' theology, concluded that “he is a thinker and exegete of resourcefulness, sharpness and originality” (RW, 116). We need to, therefore, assume that Arius did not contradict himself.
Alexander taught that there was no gap between Father and Son (RW, 189). In other words, the Son is co-eternal with the Father. The Arians did not accept this view because it would mean that there are two “unoriginated ultimate principles” (two Beings who exist without cause and which gave existence to all else), which all agree cannot be (RH, 57). Furthermore, they argued that the titles “Father” and “Son” mean that the Father gave existence to the Son (RH, 57).
Arius, in contrast to Alexander, taught that a gap exists between the Father and Son.
Alexander attempted to force the Arians to admit that the phrase “He was not” means that there was a gap of normal time when the Son “was not.” (RW, 189)
However, Arius wrote that it is not a gap of normal time. Arius said that the gap is “logical,” and if that gap involves some literal time, then it may be “an infinitesimal reality.” (RW, 189) Arius does not want to use “the same sort of language for the 'interval’ between Father and Son as for that between creator and creature more generally” (RW, 189).
Williams also explained the Arian view as follows:
“Faced with the notion that there was no 'interval’ between Father and Son, Eusebius (of Caesarea) is not necessarily being inconsistent in stressing the Father's pre-existence. From our point of view, in the world's time, Father and Son co-exist; from the Father's point of view, so to speak, they do not and cannot.” (RW, 172)
Perhaps we can rephrase Arius’ view as follows:
This universe, including time, was created through the Son. But, beyond our universe of time, space, and matter, exists an incomprehensible and timeless infinity. In that ineffable infinity, the Son was begotten. Therefore, there was no literal “time” before the Son was begotten. From the perspective of our existence within time, the Son has always existed.
This article is largely based on two books:
The Search for the Christian doctrine of God - The Arian Controversy 318-381, 1987 by Bishop RPC Hanson (Referred to as “RH” in this article)
Arius: Heresy and Tradition - by Archbishop Rowan Williams, 2002 (Referred to as “RW” in this article)