Many say we can't....but not everyone.
Scientists are finding that Octopuses & squids are evolving rapidly (https://www.sciencealert.com/octopus-and-squid-evolution-is-weirder-than-we-could-have-ever-imagined). Apparently, they are routinely changing their DNA to adapt to their environment. The article discusses it as if it is a rarity. I googled it to see what a quick search would find around humans changing their DNA. I found this - https://www.heartmath.org/articles-of-the-heart/personal-development/you-can-change-your-dna/ which holds that, indeed, we can change our DNA. The organization that found that - Heartmath (which started out of Princeton btw) - is a REALLY cool organization. If you're up on your epigenetic and quantum physics chatter, it'll be right up your alley.
Here's what's interesting - quantum physics? There are scientists who don't believe in it. I chatted up a pretty heavy-duty neurologist once and he held that quantum physics was pretty much crap. Is he right? Or just unaware? Bruce Lipton (and MANY others) wrote books that support it and discuss research along with that. It's an interesting debate - CAN we change our DNA or not? I've read the articles & books, and learned HOW to change DNA through energy work (quick note - to be fair, while I believe it's changed, and have SEEN the changes in people and their physical and energetic bodies, I have no DNA researched back-up for that...but yeow, wouldn't that be cool to do?!), so I'm a believer. But that's me.
Here's the thing; does it really matter? It goes back to one of my core beliefs - that science does not know everything. Today they say that we all have DNA and we get it from our genetics, and we're destined to do/be what it holds. I give that a firm "meh". As I said in my first blog - we are a planet of 7.8 billion people, and getting a list of how we ALL operate is just not cost effective. So we really don't know. And to take a sample of even a huge 100,000 for scientific research (which I understand is quite rare - here's a discussion of sample size: https://www.sciencebuddies.org/science-fair-projects/references/sample-size-surveys) is rarely done, AND even that is a TINY percentage of the population. Plus it assumes that we're all basically alike. You can look at a diverse group of people in a room and know that's untrue.
So again, what ELSE don't we know? What ELSE are we believing, potentially to our detriment? Hmmm......