The category in the customizer will be listed according to the order of the category in the backend. So there is no feature to change the order in the front end.
However, you can use the third party plugin to change the order of the category in the backend which helps you change the order in the front end. There are lots of plugin for this and below is one of them.
It requires higher code customization so are unable to help you with this.
As a workaround, you can create the category yourself in order that you want to display in the front end. This might help you as for now. The newly created category will be listed at the top and will be displayed according to in the front end as well.