This topic has been discussed to death on forums since The Witcher originally came out: At first I rejected the idea, because practically there were to many loopholes.
Then someone convinced me that Alvin is the GM based on what is being given you from a stroyteller's perspective.
Yet, if you sit down and work out the nitty-gritty of how it could possibly have worked in practice, even taking magic into account; it still doesn't make sense that the adult GM doesn't seem to realise that the child Alvin is he himself. (Or perhaps he does, some other posters seem to think).
Surely the only way this could work, is that Alvin traveled to some point about 30 years into the past, and then grew up to be the GM, who seems around 40, 45, 50 years old. Yet, he must know that the child Alvin is he himself. So one has to assume then, that the GM wants things to happen the way it does, up to the loop where Alvin transports himself back in time.
In a way, this would create an impossible cycle. The GM made Salamandra steal the secrets at Kaer Morhen, in order to create a super mutated army. The Salamandra were also stealing children to experiment on, and grabbed Alvin, which caused Geralt to save Alvin, and assume co-guardianship of him.
But if the GM had not initiated all these doings, Geralt would not have investigated the Salamandra, and Triss would not have teleported both Alvin and Geralt to safety as in Ch. 4, and Alvin would not have transported himself to safety when the nonsense hit the fan in Ch.4.
So, if Alvin had, in ch 4, really transported himself back to some point in the past where he would, from that point, grow up to be the GM of the present, he himself would have, as the adult GM, precipitated his own transportation back into the past, which to me seems to create a sort of a cause-and-effect impossibility, if you go and sit down, and make a flow diagram out of the whole thing.
Look, I can see Conn tried to circumvent the problem presented by the conundrum that I have sketched above; the problem of what was first, - the chicken or the egg, by making the first timeline sans Geralt. ..but the circles going round and round in time still don't really make sense if you draw a diagram, or shall i say, a flowchart of them, because why would Alvin choose to allow himself to get into the same situation - a loop, time and again, if he as the GM knows what happens to Alvin?
Sure, you could say that the GM puposely engineers Alvin to keep making a loop back in time; but that just also doesn't make sense. These powers that the sources have, seem to be quite random- and especially if used by a child untrained in these powers such as Alvin was, how could he be sure he would land up in exactly the same place in the past every time? If he landed at just a slightly different spot in time, that should be enough to change the course of the "future".
Although I can see that storywise, the devs probably meant for Alvin to be the GM, in a practical sense of the logic of the thing, it just doesn't work for me.