Lucky you, you're coming with me, regardless of your ancestry - you want to do your own trip fine, but we're going on mine first. Our trip would begin at Lake Turkana in the Rift Valley in East Africa, in northern Kenya. And already the trip is difficult, because now we would have to start walking north, like our ancestors did, into Ethiopia. Not only is this a searing parched desert (although not necessarily any hotter and drier than it was when great grandma left - she was tough), the rural areas of northern Kenya and the border with Ethiopia are also not at all a safe place. People doing normal trips for legitimate reasons require armed military convoys to make the journey safely. And as I write this, the whole region seems poised to become a war zone; it's even less safe today than when I first thought of this. (We're not even out of the first country and I've already provided multiple good reasons not to do it.)

Above: the sort of fellows we don't want to meet, but probably will if we're just out walking around. Below: more fellows we don't want to meet, but probably will.
After we walk into Ethiopia, we cross the Blue Nile on a log (and get schisosomiasis, assuming the crocs don't get you, which they probably would - great grandma had a set of cajones on her too) and start walking along the river's eastern bank until we get to Egypt. I've walked well over 2,000 miles through the hottest deserts on Earth at this point. We now enter Asia at the Sinai Peninsula. Congratulations, you've made it to 40,000 BC, when more humans started leaving Africa, following the example set by the ancestors of the Aboriginal Australians (who got there already by at least 60,000 BC.) If my wife had also been along for the trip, at this point, we would part ways: she starts walking northwest to China across the deserts and mountains of Central Asia. It's worth noting that at that point, our great grandma (yes, for both her and me) still had dark, African-looking skin. The skin adaptation occurred amazingly late even in cloudy high latitude places - the friendly pre-Indo-European fellow you see below (Cheddar Man) was a resident of the British Isles 10,000 years ago. (And if you think Britian is cloudy now, remember this is the end of the ice age.) Congratulations, it's now 20,000 BC and we're wandering through eastern Turkey, then around the eastern edge of the Black Sea, which at some point around now, actually became a sea.
At some point we enter actual history when we encounter Julius Caesar's legions above the Rhine, but it's okay; we kick Varus's legion's ass in the Teutoborg Forest in AD 9 (we find some Italian visitors and also buy them beers.) Maybe we get a nice AirBNB on an old farm east of Basel, where I'm now maybe a nice loyal farmer in the Roman province of Helvetia. (Note: I'm almost entirely of Swiss and German descent. Lucky for me. If you're a typical American mutt, you'd have to decide to follow just one ancestral line, or you'd be retracing multiple last few centuries of your ancestry.)
Above: buying beers for Italian tourists. I'll be honest with you, they suck at wall upkeep as well.
After a few more nights passing the medieval period, we ride to Basel (now I'm a greatx~5 grandfather whose name I actually know), then take a boat from there to Rotterdam - and finally a bigger boat, to Philadelphia! We ride a horse up to old Berks County (like William Penn did about 50-60 years before.) We hang around in Berks for a few centuries, and finally, I'm myself! I can drive to California like I did at the tail end of the twentieth century. And I'm home.
After thirty years of thinking about this, I am choosing not to do it. I'd rather actively decide it won't happen, then wistfully pine for "someday". At a certain age you have to admit to yourself, a lot of somedays are turning to nevers, and I want to choose which ones. And I'm choosing this one not to do. The actual experience of this is not likely to balance out against the logistical nightmares, red tape of getting a horse across multiple national borders, the cost, as well as passing through places with severe threats to health and safety that show no sign of resolving.