Yes! Cooperation seems to be just as fundamental, if not more, than competition. We wouldn't have gotten volcanic islands to break down into soil if it weren't for the partnership that is lichen. We wouldn't be able to digest a tenth of what we're able to eat if it weren't for our gut bacteria. We wouldn't have trees if it weren't for mycorrhizal fungi which over 90% of plants depend on.
There's a famous paper/framework called "Major evolutionary transitions in individuality" that sketches out a big picture pattern of major evolutionary advances in complexity following a surprisingly consistent pattern: As cooperation and division of labor strongly increase, selection starts working on larger entities. This pattern holds all the way back to the origin of life itself as things moved from self-assembling molecules to compartmentalized populations of molecules, from replicators to chromosomes, from RNA+enzymes to DNA+proteins, from prokaryotic cells to eukaryotic cells, from unicellular to multicellular, from individuals to colonies/superorganisms, and (possibly) onwards to more complex societies
> Cooperation seems to be just as fundamental, if not more, than competition
Both are fundamental. You can't survive without cooperating, but you also can't survive if you try to cooperate with the entire biosphere because ultimately there is competition for scarce resources. If you don't assert yourself to claim your share of those, something else will.