Apes are not greedy, and neither were humans in the Paleolithic Era. Before the invention of the technology of agriculture and the building of permanent villages, there was no way for a nomadic hunter-gatherer to amass an unusually large collection of possesions. He had no way to carry them: no domesticated riding or draft animals, no wheels.
You don't see other species of apes exhibiting greed. Sure, if there's a famine and there's not enough food, one tribe will defend its gathering territory (we are the only carnivorous ape so the other species don't hunt) from intruders, but within a community the members cooperate with each other. Stone Age humans behaved exactly the same way.
But we are a pack-social species and our goal is to spread the genes of the community, not the individual.
You need to study the Stone Age in a lot more detail. Most of what you think you know about it is dead wrong. Humans are not equipped to survive easily as individuals, the way tigers and other solitary hunters are. Our physical strength and our senses of smell and hearing are not adequate for a single person
with Stone Age tools to bring down enough game to comprise a satisfactory diet.
We use our uniquely superior intelligence (our forebrain is more than twice as large as any other ape relative to body size, and it's immense compared to all other warm-blooded animals) and our unique communication skill (no one knows when the technology of spoken language was invented but it almost certainly goes back to at least 70KYA, before we migrated out of Africa) to cooperate in clever ways. The power of the tribe is much, much greater than the sum of the powers of its individual members. One human with a spear is lucky to bring down a beaver. Twenty humans can bring down an entire herd of deer or goats.
Humans have always cared for and depended on the few dozen members of their extended-family or "pack," people they've known and trusted since birth. That's an instinct programmed into our neurons by our DNA. The miracle of our development since the Neolithic Era (the dawn of agriculture) is that we've been able to
override that instinct and redefine our "pack" to include a larger and larger group.
In the first farming villages the pack included a few neighboring tribes whom we invited to join us because the economy of scale and division of labor made possible by a larger village increased productivity, and freed up a few people from "careers" in the food production "industry" to do other things such as building houses or composing music. These people were not total strangers, but they were not exactly "family," yet we learned to live in harmony and cooperation with them
because it made us all more prosperous.
The next step was the building of cities. In cities we had to learn to live in harmony and cooperation with total strangers. We had to respect the authority of a leader who was not our own grandpa. Once again, we were able to override our instinct and accept these people as pack-mates because it made us even more prosperous. We now had formal musical performances, fancy clothing, animals bred for racing, social dances, beautiful ceramics, alcoholic beverages, and other activities not directly needed for survival.
We kept enlarging our "pack." Next it became a state, a large group of people, most of whom never met each other, but shared a common language and culture and respected the same leaders. Then it became a nation, then an empire, and then a trans-national hegemony such as the EU. At each step the benefits of accepting more distant strangers as pack-mates were so great and so obvious that we were willing to live a life that was not exactly synchronized with our instincts. And we were able to do this only because of our enormous forebrain, which gives us the ability to modify or override our instincts. It's obvious that the next step will be a single global civilization, one "pack" including all of us. The added benefits will be astounding. Just never having another war will enrich us by a couple of orders of magnitude--look at all the effort and resources we waste, protecting ourselves from each other! The prosperity of that era is unimaginable.
The reason we help other people is that
over the past twelve thousand years we have learned that helping other people enriches our own lives.
We're not monkeys, content with a place to sleep and leaves to eat and a few simple games. We very much enjoy our modern life with its comfortable furniture, its climate-controlled homes, its inexhaustible variety of fantastic food, its transportation technology that allows us to see both the natural and man-made wonders in other lands, its communication technology that allows us to have friends on the other side of the planet and enrich ourselves by discussing our different cultures and ideas, its modern scientific medicine that allows us to build a family by having only two children instead of having ten and weeping as eight of them die, its dozens of domesticated animal species so we can form bonds with dogs and cats and parrots and capybaras and discover an entire new dimension to the universe inside our heads and hearts, and of course its inexhaustible supply of entertainment.
I don't know about you, but for me that's more than enough reward to convince me to be nice to other people.
Anthropology is a science and nothing in this post is the least bit controversial to an anthropologist--except possibly the timing of the invention of language, and as an amateur linguist I'll pull rank on the professional anthropologists.
You need to delve a little deeper into the sciences. You'll find that a lot of your questions have already been answered.
Anthropology would be a great place to start. Work your way from the Paleolithic Era (nomadic hunter-gatherers) to the Neolithic (people settling in one place and practicing farming and animal husbandry) to city-building (strangers learning to work together and respect authority, domesticated animals to augment our own musclepower) to the Bronze Age (metal tools that revolutionized nearly every aspect of life but also made war possible, written language, money, wheels that allowed us to travel more widely and trade goods and ideas with distant cities) to the Iron Age (not merely better metal tools but a quantum improvement in technology that created a civilization that we would recognize today with highways and sewers) to the Industrial Revolution (conversion of the chemical energy in fossil fuel into kinetic energy increased the productivity of human labor so tremendously that 99% of the human race were no longer doomed to "careers" in food production and distribution, motorized transportation that took everybody everywhere) to the Electronic Revolution (instant communication among all people everywhere, breaking down the last boundaries between our various "packs").