Your scenario already happened. Look where the black civilizations in Africa advanced to and where the European civilizations advanced prior to European contact with Africa for your answer, and actually, the blacks had the advantage of having a bigger continent with more resources than the Europeans had and the Europeans still won.
What resources are you speaking about exactly? I would suggest you read Guns, Germs and Steel.
"In our earliest societies, humans lived as hunter-gatherers. The first step towards civilization is the move from hunter-gatherer to agriculture, with the domestication and farming of wild crops and animals. Agricultural production leads to food surpluses, which supports sedentary societies, specialization of craft, rapid population growth, and specialization of labor. Large societies tend to develop ruling classes and supporting bureaucracies, which leads in turn to the organization of empires.
Although agriculture arose in several parts of the world, Eurasia gained an early advantage due to the availability of suitable plant and animal species for domestication. In particular, the Middle East had by far the best collection of plants and animals suitable for domestication barley, two varieties of wheat and three protein-rich pulses for food; flax for textiles; goats, sheep and cattle provided meat, leather, glue (by boiling the hooves and bones) and, in the case of sheep, wool. As early Middle Eastern civilizations began to trade, they found additional useful animals in adjacent territories, most notably horses and donkeys for use in transport.
In contrast, Native American farmers had to struggle to develop maize as a useful food from its probable wild ancestor, teosinte. Eurasia as a whole domesticated 13 species of large animals (over 100lb / 44 kg); South America just one (counting the llama and alpaca as breeds within the same species); the rest of the world none at all. Diamond describes the small number of domesticated species (14 out of 148 "candidates") as an instance of the Anna Karenina principle: many promising species have just one of several significant difficulties that prevent domestication. For example, horses are easily domesticated, but their biological relatives zebras and onagers are untameable; and although Asian elephants are tameable, it is very difficult to breed them in captivity.
Eurasia's large landmass and long east-west distance increased these advantages. Its large area provided it with more plant and animal species suitable for domestication, and allowed its people to exchange both innovations and diseases. Its East-West orientation allowed breeds domesticated in one part of the continent to be used elsewhere through similarities in climate and the cycle of seasons. In contrast, Australia suffered from a lack of useful animals due to extinction, probably by human hunting, shortly after the end of the Pleistocene. The Americas had difficulty adapting crops domesticated at one latitude for use at other latitudes (and, in North America, adapting crops from one side of the Rocky Mountains to the other). Africa was fragmented by its extreme variations in climate from North to South: plants and animals that flourished in one area never reached other areas where they could have flourished, because they could not survive the intervening environment. Europe was the ultimate beneficiary of Eurasia's East-West orientation: in the first millennium BC, the Mediterranean areas of Europe adopted the Middle East's animals, plants, and agricultural techniques; in the first millennium AD, the rest of Europe followed suit.
The plentiful supply of food and the dense populations that it supported made division of labor possible. The rise of non-farming specialists such as craftsmen and scribes accelerated economic growth and technological progress. These economic and technological advantages eventually enabled Europeans to conquer the peoples of the other continents in recent centuries by using the "Guns" and "Steel" of the book's title.
Eurasia's dense populations, high levels of trade, and living in close proximity to livestock resulted in widespread transmission of diseases, including from animals to humans. Natural selection forced Eurasians to develop immunity to a wide range of pathogens. When Europeans made contact with America, European diseases (to which they had no immunity) ravaged the indigenous American population, rather than the other way around (the "trade" in diseases was a little more balanced in Africa and southern Asia: endemic malaria and yellow fever made these regions notorious as the "white man's grave"; and syphilis may have spread in the opposite direction. The European diseases the "Germs" of the book's title decimated indigenous populations so that relatively small numbers of Europeans could maintain their dominance."