My question deals primarily with human beings - can scientists see if a person's DNA has been genetically modified? If so, how? If not, why not?

In my story, the protagonist finds he is immune from most diseases and he can easily and quickly heal from bad cuts or broken bones in a matter of minutes or days (depending on what kind of injury we're talking about) after surviving a shootout that should have left him paralyzed. His leader doesn't think his survival is a fluke, so she has his DNA tested, suspecting genetic modification played a role in the protagonist's immunity.

After her scientists run tests for her, she surmises that the protagonist's DNA had to have been tampered with before even his conception.

Does this seem at all feasible, to be able to see through tests that someone's genetic code has been altered - or even to go so far as to learn in what stage of the person's life these alterations occurred? I guess slightly on this same vein of topic: Would a scientist be able to see if someone's telomeres were longer than usual, or that they had more mitochondria in their cells? How would someone see this?

I didn't find the right solution from the internet.
References: https: //able2know.rg/tpic/
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