I think this would most accurately describe what you are trying to convey. If we try to see through each others eyes we can make the world a better place.

"if everyone truly put oneself in the others' shoes, the world could get better" - If everyone truly put themselves in one another's shoes, the world would be a better place. - If everyone truly put themselves in each other's shoes, the world would be a better place.

Couple of options for how to word it. "The world would be a better place if we put ourselves in each other's shoes." "If we put ourselves in each other's shoes the world would be a better place."