How install macOS WITHOUT the original Appl

That Mac cannot boot to Internet Recovery Mode. The feature was first introduced with Macs that shipped with Lion, 10.7.x.

You don't want the previous owner's information on the Mac at all. Since you don't have the original gray disks, you can purchase the retail version of Snow Leopard from Apple for $20.

Once you get the disk, put it in the drive and restart. Immediately hold down the C key to boot to the disk. As soon as you can get to the top menu bar, choose to run Disk Utility.

In Disk Utility's interface, click on the very far left drive name. Choose the Partition tab at the right. Where the drop down menu says "Current", change it to "1 Partition". You need to do this, otherwise the hidden recovery partition will not be removed from the drive. When you choose 1 Partition, the Options button at the bottom will now be active. Click on that to make sure the partition scheme is GUID. Click Apply. It will only take about 15 seconds to wipe the drive clean.

Exit Disk Utility and choose to install the OS. Once Snow Leopard is installed, the Mac will restart to the hard drive and automatically launch Software Update. Let it install the 10.6.8 update. Uncheck all others. There's no reason to wait for the other updates when you're not staying in Snow Leopard anyway. 10.6.8 will put the App Store on the drive, which is the main reason for applying that particular update.

When that's done, launch the App Store. Login to your account, or create one if you don't already have an account.

Go to this page. Scroll down to the Get OS X El Capitan link. Follow the instructions to download and install El Capitan.

If the iMac doesn’t have an OS installed, or one less than 10.6, you need to use a disk to install or upgrade the OS.

If the iMac is running 10.6 through 10.6.7, use the Software Update pane of System Preferences or Apple’s website to download 10.6.8.

If the iMac is running 10.6.8 or above, click here.

The message you got typically comes when people try to install or reinstall the OS, not upgrade it.

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You also need at least 2GB of RAM.

From OWC…

Details: *This system can run the last version of OS X 10.8 "Mountain Lion", OS X 10.9 "Mavericks", OS X 10.10 "Yosemite" and OS X 10.11 "El Capitan" -- if upgraded to at least 2 GB of RAM, including booting in 64-bit mode. However, it does not support OpenCL nor does it support AirDrop, AirPlay Mirroring (which also requires a 2nd Gen or later Apple TV), Power Nap, or other advanced features. It is not capable of running macOS Sierra (10.12) or subsequent versions of the macOS at all.

The reason you are having issues is your iMac is too old to support Sierra.

MacOS Sierra - Technical Specifications

El Capitan is the latest if you have the right model. Otherwise Yosemite.

Actually you would need the original install disks. Or purchase Snow Leopard or Lion from Apple's Store.

I think your iMac is too old for internet recovery. But perhaps someone else will answer.