The installer must be downloaded from App Store, and you need an Apple ID with a payment method (Credit card). You can select "None" as payment method, but then you cannot download!

The App Store link for High Sierra is
macappstores://apps.apple.com/app/macos-high-sierra/id1246284741?mt=12

Links to other versions in the App store can be found at https://support.apple.com/en-us/HT211683

After the download it will start the installer.

To create a USB key with the installer:

• cancel the installation
• insert USB key
• set the name of the USB key in a variable:

  name=U # <== Volume name (eg. "USB_Installer")

• Run

  sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/$name

or with other versions or methods, maybe adding the --applicationpath option is useful?

sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ macOS\ High\ Sierra.app

This step is probably unnecessary, because the installer does the formatting?

diskutil list | grep -A6 external
disk=disk4; name=USB_Installer     # <== Define variables
diskutil eraseDisk HFS+ $name $disk

This one might only get a small stub instead of the full image: https://apps.apple.com/us/app/macos-high-sierra/id1246284741?mt=12

To get the full installer:

• Start the installer, which will download missing stuff
• Quit when prompted to restart
• Copy downloaded files to the right place :

sudo cp -pRv "/macOS Install Data" "/Applications/Install macOS High Sierra.app/Contents/SharedSupport"

Or directly download the missing stuff:

File list: https://swscan.apple.com/content/catalogs/others/index-10.13-10.12-10.11-10.10-10.9-mountainlion-lion-snowleopard-leopard.merged-1.sucatalog.gz

• BaseSystem.dmg
• BaseSystem.chunklist
• InstallInfo.plist
• InstallESDDmg.pkg
• AppleDiagnostics.dmg
• AppleDiagnostics.chunklist

Or :

url=http://swcdn.apple.com/content/downloads/29/03/091-94326/45lbgwa82gbgt7zbgeqlaurw2t9zxl8ku7
curl -R --remote-name-all $url/{BaseSystem,AppleDiagnostics}.{dmg,chunklist} $url/Install{Info.plist,ESDDmg.pkg}

This forum post (or this page) suggest using softwareupdate. It didn't work for me, but may be worth trying:

softwareupdate --list-full-installers
softwareupdate --fetch-full-installer --full-installer-version 10.13.6 # adapt version number

https://www.insanelymac.com/forum/topic/329828-making-a-bootable-high-sierra-usb-installer-entirely-from-scratch-in-windows-or-linux-mint-without-access-to-mac-or-app-store-installerapp/

https://apple.stackexchange.com/questions/299731/macos-high-sierra-media-installer

https://apple.stackexchange.com/questions/324710/install-macos-high-sierra-app-does-not-appear-to-be-a-valid-os-installer-applica

Apple's How to create a bootable installer for macOS :

sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume