An instance of DateTimeFormat can do Date -> string but cannot do the reverse string -> Date for formatted strings it created.

It's very hard to implement that in user-land because different browsers might handle different languages in different ways?

My proposal is a parse method that is reverse of the format method:

const x = new Intl.DateTimeFormat(/* format options */);

// true, assuming format options are lossless
x.parse(x.format(aDate)).getTime() === aDate.getTime()