How to set a default value for components?

Question

Vue.js

There are two components Tabs and Tab , Tabs acts as a control for a group of several Tabs, it looks like this .
Is it possible to make it so that when the v-model is empty, the first Tab is set by default? I tried to implement this in the setup of the Tab component:

...
  setup(props) {
    const tabsGroupValue = inject("tabsGroupValue");

    const isSelected = computed(() => props.value === tabsGroupValue.value);
    
    if (!tabsGroupValue.value)
        tabsGroupValue.value = props.value;

    return {
      tabsGroupValue,
      isSelected,
    };
  },
...

This works, but for some reason the last Tab is set by default, and not the first. Is there any way to fix this?