but when actually looking through the start menu or the Windows search, it's nowhere to be found.
To solve this problem you can copy the blender shortcut and go hit the
WindowsKey+R or search for
Run. Next type
%appdata%\Microsoft\Windows\Start Menu\Programs and hit enter. Then a folder will open, just paste the shortcut into the folder and it should show up in your search bar.
Next time please ask questions as such on https://superuser.com/
This has probably happened as you downloaded the ZIP file instead of the Installer(.msi) file. If you download the installer instead it will put the icon into the menu and you will be able to search for it.