Without access to an old mobile device running iOS 10 or earlier, is it possible to download 32-bit apps

No. There isn't a public directory of urls for older versions of an application.

It is in the realm of possibility, that you could use an old version of Xcode on an old version of macOS instead a VM on your M1 using UTM. (This alone will be complicated and take hours to set up). Once you are on a version of Xcode that has an iOS emulator supporting iOS 11. You may be able to download it to the phone.

Making use of the application may also be difficult. Apple discontinued 32 bit apps in iOS 11. So even if you found the binary, you can't run it on any iOS 11+ device. Apple also discontinued 32 bit apps on Catalina, so you can't run it on an M1 system.

Without access to an old mobile device running iOS 10 or earlier, is it possible to download 32-bit apps

No. There isn't a public directory of urls for older versions of an application.

It is in the realm of possibility, that you could use an old version of Xcode on an old version of macOS installed inside a VM on your M1 using UTM. (This alone will be complicated and take hours to set up). Once you are on a version of Xcode that has an iOS emulator supporting iOS 10. You may be able to download it to the phone.

Making use of the application may also be difficult. Apple discontinued 32 bit apps in iOS 11. So even if you found the binary, you can't run it on any iOS 11+ device. Apple also discontinued 32 bit apps on Catalina, so you can't run it on an M1 system.

Apple discontinued 32 bit apps in iOS 11. So even if you found the binary, you can't run it on any iOS 11+ device. Apple also discontinued 32 bit apps on Catalina, so you can't run it on an M1 system.

Without access to an old mobile device running iOS 10 or earlier, is it possible to download 32-bit apps

No. There isn't a public directory of urls for older versions of an application.

It is in the realm of possibility, that you could use an old version of Xcode on an old version of macOS instead a VM on your M1 using UTM. (This alone will be complicated and take hours to set up). Once you are on a version of Xcode that has an iOS emulator supporting iOS 11. You may be able to download it to the phone.

Making use of the application may also be difficult. Apple discontinued 32 bit apps in iOS 11. So even if you found the binary, you can't run it on any iOS 11+ device. Apple also discontinued 32 bit apps on Catalina, so you can't run it on an M1 system.