As someone who has tried to get the non-VAT US prices - you need a credit card issued in the country you claim you’re from before downloading any apps.
That's if you plan to pay. You can download free apps without a credit card. I changed my app store country from Russia to the US this way because I got fed up with some free apps being unavailable because reasons.
But even if you do want to pay for things, I suppose you can make a second account for the desired country, activate your iPhone and set up alternative app stores with that, and then log into your real one.
