Henry's first departure happened when he was six years old; that thus makes this the first trip to the past. We know that he later will travel to an earlier time, and that Alba too will travel to earlier times, but since these trips originate from later in history they cannot occur until after Henry makes this one.
Nor can an older Henry appear with a blanket and an explanation, because Henry has to grow older before he can make that trip.
Thus sometime around Christmas 1969 when Henry was six he was riding in the car with his mother when she lost control on the ice. He vanished, leaving his clothes in the back seat of the car, stood naked in his own home for a moment about two weeks in the past, then reappeared standing on the street roughly where the car had been, completely devoid of clothing. He saw the fiery crash that killed his mother, and was found by emergency services, shivering by the side of the road. They'll have wondered about his clothes, but his explanation will not make any sense: he was in the car, the car started going out of control, for a moment he was home, and then he was standing in the street. They will assume he blacked out. They might even tell him so, that the moment when he was home was all a dream, that somehow either he fell from the car when the door popped open or his mother managed to toss him from the car to safety, although no one understands what happened to his clothes.
There is then a serious gap in our knowledge: we never see the child Henry travel in time again, but at some point a young Henry must make the trip which brings him the blanket. This Henry looks like the one who works in the library, but he looks much like that up to the day before he marries Clare. However, we also know that he vanished from that library on Christmas Eve one year, and that he makes a comment about how long it took to do what he was doing in the stacks. It seems likely that this trip is the only other one about which we have any certain knowledge to take place prior to meeting Clare. That still leaves us with a significant gap, because that Henry already understands that he is traveling through time. That suggests that there has been at least one and probably several other temporal trips by which he has learned this.
It is not that difficult to grasp how he understood this, though. He later tells his father that he has seen his mother die "hundreds of times", and that before he proposes to Clare. Even supposing that to be wildly exaggerated, to have returned to the moment of the accident as often as twice and been in the past long enough to see more, and to see from a different location, and to see that he was not that child whom he sees standing on the street, would be sufficient to tell him that these fits are real movement through time and space; and two more to other times and places would confirm that it is not a psychotic reliving of a memory. It would also teach him the futility of trying to change the past, because he would be unable to stop the accident. History would change, indeed, but only so much as by the number of copies of Henry de Tamble watching it happen.
Then one Christmas he vanishes from the library, and finds himself in the past with enough time to steal some clothes and a blanket and arrive at the accident scene to wrap his naked younger self in something warm. He will have changed the past. However, he will also have changed his own memories of the past--now he remembers that someone claiming to be him showed up, wrapped him in a blanket, and said something about time traveling. So now he knows what he originally had to figure out for himself. That, though, does not destroy time. Although it is a predestination paradox, it is the sort in which it is only information that becomes its own source. Whether Henry told himself he was a time traveler or not, Henry will still be able to tell himself by the time that moment arrives. We erase the histories in which he deduces this from experience, and replace them with histories in which he begins with an explanation.
And, having changed the past, he does not know he did so, because the only past he knows is the one he himself created.
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