Yes, we know that we virtually can't, at least not in a long-term multi-generational societal context. Humans are superbly evolved to eat a little bit of just about everything, and terribly evolved to eat a lot of one kind of thing for a long time. There are millions of years of evolution built into us and inherited from our ancestors that determined that a modern homo sapien is destined to require some animal products in their consumption inventory. Meat was important enough that if we had an herbivorous ancestor, that ancestor is unknown in the fossil record. We purposely spent so much time finding animal sources, despite plentiful plant life nearly everywhere, that we even evolved brains, tools and fire and actually evolved away in-situ nutritional synthesis of various critical nutrients (that all other herbivores enjoy) all almost purely to take on the higher risk task of eating other animals. https://news.ycombinator.com/item?id=7763330
In theory it might be possible to craft a healthy, sustainable, long-term diet that uses no animals whatsoever, and would last generations with no ill effects on population health.
However, there's overwhelming evidence that, in practice, the kind of diet around 90% of practicing vegans practice is not that diet. In numerous serious studies, 70-90% of all tested practicing vegans test as B12 deficient, which is not a sustainable long term dietary deficiency over generations. Theoretically, after just a few generations of this kind of deficiency, if anybody is alive at all, they'll suffer from severe congenital neurological deficiencies that would make sustaining a modern society impossible. B12 sufficiency would be a non-optional part of any non-animal diet, and it appears that practicing vegans are not able to construct an alternative herbivorous diet that provides even single-generational sufficiency.
Other typical deficiencies found in large vegan population studies suggest that humans are generally poorly adapted to long-term, sustained, plant-only diets: with neurological and cardiovascular issues presenting as long-term consequences of the diet.
There's other challenges, some nutrients are pitifully rare or not as bioavailable to humans from plant sources as from animal ones: B12, DHA (and some important varieties of O3FAs, Vitamin A compounds, Arginine, Creatine, Carnosine, Vitamin D, Heme, and the list goes on.
There's other issues to, as the nutritional balance of vegan diets isn't what we're evolved to process, humans suffer from various absorption issues as plant sources provide high quantities of some food components that prevents absorption of some critical minerals: e.g. phytates block zinc for example.
One of the significant challenge for Vegans is the incredible amount of "sciency-sounding", but completely wrong nutritional advocacy advice available in the vegan community. The science is so complex, almost no vegan understands enough of the science of human biology, nutrition and agriculture to properly assemble a diet for themselves (as demonstrated through dozens of studies). Various critical dietary issues are often waived away or minimized (just eat yeast extract!) and major deficits are often covered up under a handful of dietary supplements (many of which are derived from animal sources) for long-term adherence.
The flip side of the problem is that modern food practices also provide animal sources far in excess of what we evolved to need nutritionally. You could probably eat a vegan diet 4-5 days a week, and eat a healthy omnivorous diet just for dinner the other 2-3 and easily satisfy all your animal sourced nutritional requirements and come out extremely healthy with none of the Vegan diet associated health problems. And I don't mean a huge steak for those dinners. I mean just a regular old meal with a few ounces of some animal sourced protein.