I don't think the hole in our hearts is necessarily god-shaped. It seems like more of a problem with modern society, not a problem with human nature.
In our industrial, urban, capitalist, and consumerist society, people are constantly working, constantly stressed-out, and moving around so much that it's hard to maintain relationships for more than a few years at a time. Compare this to societies that are less industrialized, more laid-back and slower-moving. People in these more traditional societies tend to be happier because they're less stressed and form tighter communities with healthier relationships.
In our modern society, the hole in the heart is caused by things like depression, trauma, an inability to find a stable romantic partner, or an inability to achieve economic stability and self-sufficiency. It's hard to find fulfillment at the upper levels of Maslow's hierarchy of needs if our basic needs aren't being met. It's hard to thrive if we can barely survive.
We don't need God to fill the holes in our hearts. We need socioeconomic equality and the right to self-determination so that each can find their own sense of fulfillment.
And God didn't fill the hole in my heart, but instead expanded it by gnawing away at me like a flesh-eating bacteria. This part has gotten a lot better since I gave up on religion. I certaily feel a lot more fulfilled without an abusive cult led by narcissists who take orders from an imaginary dictator!