When you put commas between values inside square brackets, you're invoking the comma operator, which evaluates each item in the comma-separated list, and then evaluates to the final value in the list. Thus, your code evaluates to [2], or only the third item. Generally, if you have an array-like object on the left hand side, you need to provide a single value in the following square brackets, like [0] or [1].
If you want to apply that style to the first three elements of the list, you'll have to explicitly iterate over them. For example, one possible implementation is:
const buttons = document.querySelectorAll('.big-button');
const firstThreeButtons = Array.prototype.slice.call(buttons, 0, 3);
firstThreeButtons.forEach(button => button.style.display = 'inline-flex');