Switching between the POV of two characters rapidly within a chapter I think would be unwise, it could be very confusing for the reader to try to establish who they are reading from the POV of if it switches so rapidly.
If there is exposition required whilst the amnesiac is unconscious, you could always have it so that he discovers these things whilst awake after the fact. This may add to the suspense of the story, that both the reader and the character are experiencing revelations at the same time, as opposed to the reader learning things via the stepdaughter and the main character learning them later.
If you would like the stepdaughter to be a short-term POV character, introducing her as one in the prologueprologue would not be unheard of. Her story could even start later than when the main character's story begins (such as her starting off finding the man and nursing him back to health), so long as the overlapping parts when he meets her later are made obvious so that the reader doesn't get confused.
Having the main character as an amnesiac is fine. This allows the reader and character to go through the same journey of discovery, as there is no exposition of the main character required from the start (other than the fact that he doesn't know anything).
His character can be built as the book progresses, though there will need to be at least another character that is established in order to give the reader someone to empathize with, rather than them only having an unknown person of unknown origins. That is a difficult person to root for without anything tethering them to emotion and humanity.
As for the return of memories, having them gradually come back is probably a good way of going. This will increase the tension as both the character and the reader are unsure of when memories will return or what will be learned.
Having the first memory return at the beginning of the first chapter will not be too early, however if you set the precedent that at least some partial memories are returned so soon, you will need to continue to allow memories to come back at a similar rate, such as a memory or two every couple of chapters.
It will seem a little odd if he gets a memory back so soon after losing it, and then no others return until halfway through the book. The recovery will need to be consistent so that the reader doesn't feel cheated. These can even just be mentioned offhandedly, such as if a week goes by and he mentions that he has remembered snippets of a beach, and a face, and maybe that he likes to ride motorcycles.
However, simply returning memories as and when they are needed will be a little bit Deus Ex Machina. Having unrelated memories and ones that make no sense at first until later revelations connect them would be better.