Updating from Yosemite to Big Sur

The original protocol used to secure https connections against eavesdropping was found to be insecure – and there was a big push to replace it. As a result, you may find that the version of Safari in Yosemite is simply unable to make connections to many modern https sites – including the Apple Community site, and the Apple Support article about how to get old copies of macOS.

I think you may need to upgrade in two stages.

• Use a modern Mac or PC to download the .DMG file containing the El Capitain installer – or the .DMG containing the Sierra one – onto a USB flash drive. You are not preparing a bootable flash drive, just transferring a data file. (Alternately, you could copy a bookmark to one of these installers to the USB flash drive, since these .DMGs are behind plain http links that even Yosemite's version of Safari might be able to handle.)
• Use the USB flash drive to transfer the .DMG file to the iMac (that is still running Yosemite).
• Open (mount) the .DMG file and run the installer inside to upgrade to El Capitan or Sierra.
• Now the version of OS X / macOS on your iMac should be new enough that you can use Safari to directly access the "How to download and install macOS" Support article and the Big Sur link in it. You might want to make a bootable clone backup of your El Capitan or Sierra system before installing Big Sur, just in case something goes wrong, and having a bootable backup would put you a step closer to recovering.

Please follow the directions on the site, they work. Unless you installed some worthless third party apps such as:

Antivirus

Cleaning

Security

VPN

Maintenance apps

Do you have any of those types of apps installed?

Please refer to How to download and install macOS - Apple Support (KE) then under the section called “.Use the App Store” click the. Big Sur link, downnload and install from there.