You can't tell forEach where to start, no, but you can ignore the calls you don't want:

inputArr.forEach((value, index) => {

    if (index < 1) return;

    // Code from here onward will only run for entries that aren't

    // the first entry

});

Or if you're not worried about copying most of the array, you can always use slice:

inputArr.slice(1).forEach(value => {

    // ...

});

You could also define your own forEach-style function accepting a starting index, if you liked, making it non-enumerable and choosing the name carefully to avoid conflicts.

It's also perhaps worth noting that since you're using ES2015, some of the reasons for using forEach go away a bit thanks to block scope. for is still a bit more verbose than forEach with an arrow function, but lets you start and end and increment by whatever you like:

for (let i = 1; i < inputArr.length; ++i) {

    // ...`i` and also any `let` or `const` here are scoped to

    // this specific loop iteration...

}

The part about i above is primarily a good thing, but also has a slight performance impact (at least for now) since a new i has to be created for each iteration. Not that that performance impact usually matters at all, though, and it won't be as big as calling a function a'la forEach.

Gratuitous example of the above:

const inputArr = ['a', 'b', 'c', 'd'];

for (let i = 1; i < inputArr.length; ++i) {

  // A closure to emphasize that each `i` is distinct

  setTimeout(() => {

    console.log(inputArr[ + i + ] =  + inputArr[i]);

  }, 0);

}

(Normally I'd use a template literal there, but wanted to avoid giving the impression the i behavior related to that.)