You may have a recovery partition which you could use,
As noted, there should be a recovery partition. You can access that recovery partition by holding down Command-R when you boot the Mac. The recovery partition will have the same version as what is installed.
If for some reason the recovery partition is damaged or is not there, then holding down Command-R when you boot will boot into the Internet Recovery mode...assuming your Mac has it (Macs from around the macOS Lion, aka 10.7, time frame and newer will have it). If you can boot the the Internet Recovery mode, then you will be able to download the version of the macOS that the Mac you have originally shipped with. From there, you would need to update using the versions available in the App Store (see below).
For more information about built-in recovery options of the macOS, see the following page:https://support.apple.com/en-us/HT201314
but you can also just download El Capitan from the App Store with this link.
Try the link...but I am not sure if it will work or not. Traditionally, the App Store will only have the latest version of the macOS available (in this case, Sierra, aka 10.12) UNLESS you had previously "bought" (i.e. download the free upgrade installer for 10.9 thru 10.11 or actually paid for the 10.7 or 10.8 upgrade installer) the older versions of macOS. The link did work for me, but I had "bought" the El Capitan upgrade before Sierra came out. I am not sure if it will work for someone who has not. If the link does not work, then the original poster should be able to call Apple and "buy" it through a telephone order that will then make it appear on their purchased list.