I've asked this very question of many non-American non-musicians and no one has failed to answer!
They might or might not say Zappa first, but then they inevitably say Gershwin and then maybe Scott Joplin.
When I first started asking this question in the late 80s in New York City, I expected everyone to say Gershwin but no one did.
(What's funny is that no one has named Philip Glass or Steve Reich, except musicians whom I avoided asking.)
If you learn music in grade school, one of the things you learn is "famous composers" and so you have a list of famous composers from each country that you just know - each Western country, anyway.
So if you were educated in Europe and someone says, "Hungarian composer!" you say Bartók, or "Finland!" you say "Sibelius!" even though you have just some hazy idea of how their music goes.
However, everyone everywhere remembers Rhapsody in Blue and/or American in Paris! They are groundbreaking works with memorable themes that are popular everywhere. I had heard these endlessly before I ever got to North America.
Everyone except, weirdly, Americans.
Most non-Americans get to see that clip of Gene Kelly dancing to American in Paris sometime in school. https://www.youtube.com/watch?v=o2WAMZRCbpU
In fact, yes, that's another thing -- the whole "soundtrack composer" thing. I did get a lot of Hans Zimmer answers, and another John Williams, but only from Americans.
The academic measure of a composer is about originality and influence. Carl Philipp Emanuel Bach does Back just as well as his father, Johann Sebastian Bach, and during CPE's lifetime, no one listened to JS, but now the reverse is true.
So John Williams and Danny Elfman aren't really going to get a look-in as "composers".
John Williams writes fine and memorable movie themes, but Holst's Planets (1917) has every technique he ever used, and more: https://www.youtube.com/watch?v=3OD_HzdZwKk
Even Zappa gets relegated to second-tier, because he sounds far too much like his influences, Varèse and Stravinsky.
---
Here's a fine American composer you might not know - John Adams.
Check this piece out: https://www.youtube.com/watch?v=Epea-MZ2fz8
It's based on the violin bowing techniques of the Shakers, and just sounds American! If you like bowed instruments, it's considered one of the greatest works ever written for strings.
And it's completely original. There was nothing like it before it was written.
Give it some time - it develops unlike the music you are used to, but it is tremendously dramatic in its own way, and has a beautiful slow movement after the initial turbulent start.
---
Your perception of how non-Americans view American culture is... strangely warped.
Up until very recently, non-Americans really revered American culture, perhaps more than Americans do!
I remember being in Utrecht in 2015 and turning the TV on during prime time - where one of the shows was a critical analysis of Martin Scorsese's work, where they would show short clips of his films, and then a panel would discuss them in Dutch.
Can you imagine this sort of thing on primetime US broadcast TV? "Films of Kurosawa - a critical analysis on NBC tonight!"
It's inconceivable.
The one-two punch of Bush and Trump have gone a long way towards damaging the USA brand, but Europeans still hugely respect American culture, even while we are trying to distance ourselves from American society.
