Cooperation can evolve without any trust being involved.

Evidence

The most economical strategy of all is not that of not having to bank on trust, but that of not even having to bank on manipulating cooperative arrangements, on the assumption that rational — in the sense of optimal — cooperation evolves by itself. Pat Bateson’s contribution to this volume explores some forms of cooperation in the animal world. The existence of cooperation among animals seems to suggest that cooperation may evolve without necessarily postulating trust, a belief which animals are unlikely to entertain. — Diego Gambetta, Trust - Making and Breaking Cooperative…, 2777