I don't think it could be said for every single person though, there are genetic differences in isolated rural communities who stuck together up to this day. I do not believe Tuvans, some Turkic-speaking, and Siberians had an ancestor who worked on the great pyramids, unless I am misunderstanding something here. We can say most of the world has a direct common ancient ancestor, considering Europe has been a melting pot for millenniums with various tribes from other continents, with the exception of various rural societies that have no connection whatsoever except within their own genetic groups, for instance, the relation between Siberia and indigenous Americans. Unless, you are going back to the very earliest peoples to say we're all basically the same, which isn't the case today. I'm on about classical and bronze era and distinguishing objectively different cultures, societies and their various accomplishments distinguished from other backgrounds of these eras. Just because we may have come from the same seed, it does not mean we didn't split and become our own people over time, with our own lineage of attainment as well as defeat. In other words, someone from northern Europe might have achieved something over hundreds of years in comparison to my people, even in regards to apparel, religion, philosophy, etc, and they can be proud of their distinct ethos from mine, because they held onto it. Yes, Greeks of today are a mix of different ancient Hellenic and few tribes from other European, west asian/middle eastern, north African, and likely Anatolian tribes, but they are Greek nonetheless, and hold onto their distinct ethos and accomplishments being that they are largely an apparent separate group from, let's say, Finland, and nobody else is holding onto that same pride....alright then?
The idea of having direct bloodlines to ancient people groups can be pretty tenuous. Literally every human on earth will have one ancestor who worked on the great pyramids of egypt for example.
Ancient people groups furthermore are often not clearly distinguished genetic groups. There's little evidence for example that peoples who spoke Celtic languages had a much greater genetic similarity to each other apart from the fact that they all lived in Europe.
Most of Europe's genetic structure was established by the Bronze age- and those are cultures which are known only by the names of the pottery they left behind.
I am curious, what is your exact argument here? If I'm correct, you are arguing that maybe I made the wrong assumption about my direct bloodline because they may had been intermixed with various communities in contrast to whom I associate with today, then maybe you are right, but I believe otherwise, because of scientific data that specifically says so in my genealogy, even if percentages vary slightly.