Downloading Google fi app, without changing región to USA

Hello Mystified1000,

In order to download an app, you need to be set in a region where it is offered. However you are correct, changing regions on your iPhone requires that you log out of the store which means ending your existing subscriptions and being unable to switch back for a time. There will not be a way to get around that in order to install region-specific apps.

If you do elect to change regions, details can be found at Change your Apple ID country or region - Apple Support

What to do before you change your country or region

• Spend any balance remaining on your Apple ID. If you're not sure whether you have a balance, check your Apple Account balance.
• Cancel your subscriptions and wait until the end of the subscription period. 
• Wait for any memberships, pre-orders, movie rentals, or Season Passes to complete, and wait for any pending store credit refunds to process. You can cancel a pre-order.
• Make sure that you have a payment method for your new country or region. See what payment methods you can use.
• Redownload your apps, music, movies, TV shows, and books on any devices that you might use to play or read them in the future. Some types of content might not be available in your new country or region. Learn what types of content and services are available in your new country or region.

Thanks!