That’s true to an extent, but has severe limitations. Of the five thing your parent comment listed (parents, genetics, geography, society, wider economy), only one (geography) is truly under your control, and even then it can be very hard to change depending on where you start and the other four (and more).
I object to those 5 things. Parents and genetics are one thing, but geography, society, and the wider economy are for everyone to navigate so make your own luck.
If you were born poor in a society which sees part of your genetics as undesirable or outright criminal—none of which were your choice—you’ll find yourself in very dire straits and changing your situation—heck, even knowing a better life is possible—will be extremely difficult.
It is not reasonable to tell a child sold into slavery or forced to be a soldier to “make their own luck”, that “society, and the wider economy are for everyone to navigate”. A person in the eye of storm and another in calm waters cannot navigate the same way.
People who firmly believe they above all “made their own luck” are the ones who had such a large amount of it outside their control they don’t even realise how much of it they had, like a fish unable to perceive the water.
I am not saying that it is easy or that everyone starts with the same opportunities. But you can make your own luck in any case to improve your life or at least to have a better shot at it.
If you believe that you are a victim that nothing you can do will make a diference, and therefore don't even try then you will definitely not improve your situation!
Now if you are born in poverty as an albino in Africa, orphaned at a young age, sold to slavery and then to a witchdoctor for organ trafficking are you fucked? Probably but that does not change the point. [I am pushing your reply ad absurdum to highlight that it is not a counter-argument...]