This seems likely to be Needle (1950), by Hal Clement.
From the Wiki description, we see many of the elements described.
An alien symbiote, not actually an amoeba, but sort of close in appearance (just much larger), and the presence of a fugitive.
The Hunter, an alien lifeform (when not inside another being,
resembling a four-pound green jellyfish) with the ability to live in
symbiosis with and within another creature, is in hot pursuit of
another of his kind. Both crash their ships into Earth, in the Pacific
Ocean, and both survive the crashes.
The Hunter makes its way to shore (its erstwhile host having been
killed in the crash) and takes up residence in the nearest human being
it can find (as it turns out, fifteen-year-old Robert Kinnaird)
without letting the human being know.
Healing factor (after the alien has later revealed himself to the host):
Upon arrival, the two begin to seek out their quarry. Bob is injured
by an accident. The Hunter is able to hold the wound together, but he
can't stop Bob from limping, and Bob is sent to the island doctor.
More on the healing factor, and the fugitive being Bob's father:
The Hunter is able to solve the riddle by observing the behavior of
the island people. Bob's father, known for his attention to detail and
safety, has been taking amazing risks. He is at least unconsciously
aware that an accident will have no ill consequences. The quarry
resides within him. The Hunter confirms this, and Bob and the alien
have a new puzzle—how to get the alien out of Mr. Kinnaird's body
without harming the man?
I can't find any cites for the father being involved in a NASA equivalent or rocketry in general, and my memory of the book is far too old to provide confirmation personally, but it seems pretty close all in all.