Solas is heavily implied to be the actual creator of the Veil.
Ignoring that he tells us this directly, but the memories of the other Ancient Elves in the Vir Dirthara attributed it to him as well. We are also told that Skyhold was once his fortress and implied to be the location where he created it, both from Morrigan's comments that the Veil is "Old here", it's Elven name translating to "The place where the Sky is held back" and that Gatsi mentions that the construction of the place implies it was built for a heavy duty purpose.
Andraste claiming that it was the Maker, millennia after the Veil was created, doesn't have nearly the same amount of evidence of His involvement (let alone existence) backing it up that we have with Solas being the creator of the Veil.
Not to say that Solas couldn't have stumbled upon the Veil as you suggest, but given his in-depth knowledge of how the Fade and the Veil works, as well as his being around at the time the Veil first appeared, it definitely seems to be confirmed that Solas did it and created it. While Corypheus did arrogantly claim the exact same things about having "created" the Anchor, he never showed any true understanding over or control over it, unlike that we see from Solas both before and after his power-up from Flemeth.
Implied, yes. But nothing is proven.
We should not take his claim as evidence. Also, the memories in the Vir Dirthara were fragmented. The first Spirit of Learning we meet states that another, not of the Qunari, arrived there and twisted the Librarians. It is possible that Solas also fed his mistaken account of the Veil to the Spirits of Learning while he was there. Other than that, the spirits reflect what the elvhen observed. If Solas was the first of their kind to discover the Veil's existence, and he moved it across the elvhen crossroads, then all those there would mistakenly believe that Solas created it. From their perspective that's exactly what it would look like. But other accounts state that the Fade existed in one dimension, the Real on another, and that the crossroads dimension existed between them. So there must have been natural boundaries between the Fade and the Real before Solas made his move against the evanuris.
Morrigan's comment about the Veil feeling old, and the research about where the sky was held back, could just be a reference to where the Fade ended and only the Real existed thereafter. The location of Skyhold was probably one such place where the Veil existed. Solas studied it, figured out how to manipulate it (Rift Mage). And then when he made his move he affected the Veil in a way so it would close together completely.
Gatsi was referring to the current structure, obviously. And the game states that it was built over numerous times, the last of which was by Fereldans. The Skyhold we see in Inquisition is a Ferelden castle.
Andraste's claim is more valid than Solas', since her actions are historically documented to have been accompanied by radical changes in the climate, likely due to the Maker's influence. Solas has lied about things before, and even if he is not intentionally lying presently, that still doesn't mean he isn't mistaken, as he is also known to do. Also, the explanation that it was the Maker is self-evident. The Fade runs through all of existence. How could Solas, even at his most powerful, create a magical vibration that repels a dimension of magical energy that runs through all existence, while never diminishing naturally itself? Only the Maker is capable of something of that magnitude. We have no solid evidence that Solas created the Veil. He wielded magic that manipulated the Veil, but others have shown this ability as well. Avernus, the spirit possessing Sophia, Justice.
Nothing indicates that Solas was around during the Veil's creation, which is never specified in precise terms. Only that there was a time before the Veil existed. Since Solas lived in a world where the Fade and the Real were separate, I would say the Veil predates him. The Chant claims that there was a time when there was only the Fade, until the Maker used much of the Fade's energy to create the Real, and then separated them with the Veil.
Corypheus showed some control over the anchor in Haven when he caused the mark to inflict pain on the Herald. He also stated that the anchor was permanent, which he was correct about. Not even Solas could take it from the Inquisitor to use himself. All he could do was destroy it along with the Inquisitor's lower arm. And besides, this magic is only said to be a key. Opening, closing, locking. Not creating.