Story is what happens. Plot is how it happens.
When you say you are telling a story without conflict, are you really?
Whether you hide it or move it around doesn’t remove it from the story; it’s most likely there. Even more so, there are probably a lot more points of conflict that you aren’t even recognizing.
The tension of conflict—a character wanting something and something standing in their way—is the heart of story, because when it comes down to it, it is a part of being human.