p:only-child {
  color:red;
}
<div>
  <p>This paragraph is the only child of its parent</p>
</div>
 
<div>
  <p>This paragraph is the first child of its parent</p>
  <p>This paragraph is the second child of its parent</p>
</div>

We could also mixin additonal pseudo classes like this example that selects the first paragraph within our nested div and the only-child of div.contain.

div.contain div:only-child :first-child {
  color: red;
}
<div class="contain">
  <div>
    <p>Hello World</p>
    <p>some more children</p>
  </div>
</div>