Try booting into Internet Recovery Mode using Command + Option + R instead to see if you can access a newer version of macOS online installer if your Mac is 2012+. It appears Apple has turned off the older online macOS installers. Maybe if your laptop is able to run a newer OS that installer will be available online.
If this does not work, then if you have access to another compatible Mac, then you can create a bootable macOS USB installer using the instructions in this Apple article (read the instructions carefully):
Create a bootable installer for macOS - Apple Support
A compatible Mac is one which can run the OS you want to create. For example to create a bootable macOS 10.13 High Sierra USB installer, you generally need access to a Mac from Late-2009 to mid-2018, but you can confirm compatibility by using this article as a guide (the Mac can currently be running any OS from 10.6+):
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
It really helps to know the exact model of the laptop involved. You can get this information by entering the system serial number here:
Check Your Service and Support Coverage - Apple Support
If the laptop originally shipped with DVDs, then you can use them to reinstall OSX 10.6 Snow Leopard which will then allow you to access the App Store or to access the 10.11 installer. Some models will require the gray restoration DVD while others will need the retail upgrade DVD. If we knew the exact model, we could tell you exactly which one would work.
You can also provide Apple with product feedback here regarding the broken online Recovery Mode servers:
Product Feedback - Apple
