Is it scientifically feasible to clone extinct races using the fragments of DNA in modern-day mutts?

For instance, the average European has about 20% Ancient North Eurasian (ANE) ancestry, the average Amerindian has 40%, and the average Indian has 10%

Different individuals are going to have that ancestry at different spots on their genome. Couldn't you "build a genome" from scratch that would be 100% ANE? And then make an actual person from it? Perhaps ancient fossil DNA could be used as a guide?