Can I run and install Windows 11 on Intel i7-7700k cpu?

You can still perform a clean install of Windows 11 on Intel i7-7700k cpu by using an ISO file instead of the Windows Update installer. The installer will check for the compatible CPU and TPM 2.0 and will warn you that your PC doesn't meet the requirements. However, it will often allow you to click "Next" and proceed with the installation anyway.

How to do it: Download the Windows 11 ISO file directly from Microsoft's website, create a bootable USB drive, and boot from it to install windows 11 on Intel i7-7700k processor.

Important Caveat: Microsoft states that unsupported devices will not be guaranteed to receive updates, including critical security updates. In practice, most users have continued to receive updates without issue, but this could change in the future.

Your i7-7700K is being blocked for compliance and security policy reasons, not performance reasons. You can bypass the block to install Windows 11, but the safest and most recommended path is to continue using the excellent and still fully-supported Windows 10 until its end-of-life in 2025. By that time, it will likely be a natural time to consider a platform upgrade.