But he does leave everything very much to chance. We know that, at minimum, present in Helgen were: Tullius, Elenwen, Ulfric, the boy (Haming?) and his carer, Ralof and Hadvar, and all these people escaped. Probably several other unnamed people also escaped, because it would be a huge coincidence for all survivors to be so high profile.
As you emerge from the tunnel at the end of the intro, you see Alduin flying off. We know from later encounters that he has excellent perception skills, but he either doesn't see you (or any other survivors) - or he just doesn't care. In any event, he doesn't care enough to hang around another hour or so and try to catch some of the survivors.
This is simply not the attitude of one who is determined to make sure everyone dies.