It helps that my assumptions about this story were totally wrong. This is in no way the story of why the Doctor absconds from Gallifrey, though the script makes plentiful allusions to Lungbarrow so clearly Platt sees that as a story already told. Fair enough, though as he has Susan note “there's always someone else's version”.
The first episode is a patchwork of bits and pieces from various previous sources, the little details about the Doctor's origins we already know: the Hand Of Omega floats along unnamed, there's a silent cameo by Clara straight out of The Name Of The Doctor, and even a moment that explains away how Susan could have named the TARDIS and it be the generic Time Lord name at the same time. There's even a sweet scene that calls back, or perhaps forwards, to Idris' description of their first flight in The Doctor's Wife.
Talking of Time Lords, somehow, in spite of all the other sacred cows being slaughtered and lines being crossed, Platt keeps to two of the big unwritten rules of Doctor Who fiction: at no point in this story are the Doctor's people named as Time Lords and there planet is never called Gallifrey. No one seems to know why this started but no matter how radical or revisionist the writer's inclinations might be none of them use “Time Lord” in a story set before The War Games and no one uses “Gallifrey” in one set before The Time Warrior. I'm sure there's one or two exceptions (The Empire of Glass springs to mind) but it really does seem to be a hard limit for an awful lot of writers. Not that there aren't anachronisms aplenty: there's a sonic screwdriver, the Hand, and a few bits of Gallifreyan lore get described even if they aren't named.
This visit to the very beginning is pretty brief and before long the Doctor (and he is “the Doctor” here, which is a little odd in light of how he gets named in An Unearthly Child, but I suppose he has to be called something) and Susan are in the TARDIS and taking off in a mad dash to escape the (unnamed) Chancellery Guard.
Much of the rest of the first episode plays out as a TARDIS story, a prequel to The Edge of Destruction in a way. It even has an explanation for the black sharpie inscription on the fast return switch, which is both unbelievable fanwank and rather cute.
There's a lot of “origin” material here outside of the TARDIS stuff. Since we see this story through Susan's narration we get a very sensory experience of the first time she and the Doctor walk out onto an alien world. We get to hear their first encounter with aliens and the moment when the Doctor begins his lifelong obsession with planet Earth.
The big contribution to the mythos here is, of course, Terry Molloy as Quadrigger Stoyn, this trilogy's villain. In this story he's some poor pleb the Doctor and Susan accidentally abduct (he won't be the last, of course) since he was working on decommissioning the TARDIS as they took off. He's been abducted, scarred in the process and is none too happy with the Doctor for it. He's a pretty useful contrast given that Platt takes pains to make the Doctor a rebel by his people's standards but not a hero by ours, keeping that initial TV arc intact.
Stoyn is portrayed as a by-the-book sort of no ambition who just wants to get home, a home the Doctor is dead set on not returning to. By the end of the story it becomes clear just how much Stoyn is willing to compromise to get home, a selfishness that makes the grumpy, stubborn pre-Season One Doctor heroic by comparison instead of invalidating the way he develops in the series.
So, overall: yes, I enjoyed it and it avoids a lot of the issues I anticipated it stumbling into. Its really less “The Beginning” and more “The First Adventure”, which is a much smaller hit to the mystery of how it all began.