How can I download Mac OS X El Capitan without app store?
You can't really download the OS X El Capitan installer app without the App Store.app easily. You can download the raw (unverified) pkg installer though, but to verify it and convert it to a legit OS X Installer.app App Store.app and a newer OS X system is required again. So simply downloading it on a Windows system won't help.



To solve your problem simply boot your MacBook Air to Internet Recovery Mode by holding altcmdR after turning it on.

In the OS X Utility window choose "Reinstall OS X" (or similar) which will download and install the original OS X your Mac came with (10.9 Mavericks).

After configuring your system open App Store.app and download OS X El Capitan. If you haven't purchased it previously use the answer in How to download OS X El Capitan from the App Store even if never downloaded before macOS Sierra was released or purchased is grayed out.