You can also just check browser locale, show a warning if != US as early setup step. Offer to take their email and tell them when more countries are added (and capture all the traffic to reactivate later).
Maybe I am mistaken about this, but I think the "browser locale" shows the preferred languages, not where the user lives. As such it would be the wrong information to use for this. For example, I am German and live in Germany, but my browser locale is en-US.
And on the other side, one could live in the US but have a different locale configured.
The locale can be used to have a quick guess, but it absolutely must not block using the product.