That's the behaviour implemented in lightning-tree-grid. You don't have to add anything else. If you take a look at the basic example in the documentation you'll see that the first row doesn't have the chevron, because it has no children:
The instructions for creating a tree grid with SLDS would apply if you weren't using the lightning-tree-grid base ...
To achieve what I needed I had to use a CSS property called calc() this article was useful: A Couple of Use Cases for Calc()
calc() is a native CSS way to do simple math right in CSS as a
replacement for any length value (or pretty much any number value). It
has four simple math operators: add (+), subtract (-), multiply (*),
and divide (/). Being able to ...