The copy of Sierra is not damaged, try again, do not use the mac while it is downloading or any other devices that share
the same internet connection. Read this.
If you do have an operating system on your mac and it is functioning then you can download
Sierra using this method.
How to get old versions of macOS – Apple Support
Go to Download macOS and click on macOS Sierra 10.12
This downloads InstallOS.dmg to your Downloads folder.
The next section can only be done on a mac that is capable of running Sierra,
a mac that came preinstalled with an OS later than Sierra will refuse to do the next bit.
When downloaded open to get InstallOS.pkg, double-click on
that and an installation window will open, read and follow the prompts,
this does not install Sierra but uses the InstallOS.pkg to create the
Install macOS Sierra.app which you will find in your Applications folder.
(If the installation window asks which disk you want to install to, you must pick
the disk that you are booted to at the time. Not any internal or external disk that
you want to eventually install Sierra on, that is for later.)
There is a problem with making a bootable USB installer with the Install macOS Sierra.app
where it returns an error Volumes/<USBname> is not a valid mount point. There is a workaround.
With Install macOS Sierra.app in your Applications folder open Terminal.
Paste in this command
sudo plutil -replace CFBundleShortVersionString -string "12.6.03" /Applications/Install\ macOS\ Sierra.app/Contents/Info.plist
press return
enter your password
press return
now paste in the createinstallmedia command for Sierra where MyVolume can be replaced with the name of your USB stick
If your USB name has more than one word separated by spaces you would need to type it in as
/The\ USB\ Name
sudo /Applications/Install\ macOS\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ macOS\ Sierra.app
press return
follow the prompts
Having made the USB installer you need to boot to it.
Restart your mac while pressing the option/ alt key when you see the Startup Manager select the USB
and press Return.
When you boot to the USB you will see a Utilities panel click on Disk Utility and press Return.
Highlight the Disk not any of the indented Volumes then Click on Erase.
Give the Disk a name.
Format: Mac OS Extended (Journaled)
Scheme: GUID Partition Map
Click Erase.
When Done quit Disk Utility.
Your mac will now have one single partition.
Click on Install OS to install macOS Sierra.
Once installed you can then transfer back your data from the Time Machine Sierra back up you made earlier,
do not transfer anything from the Mojave partition back up.
