How can I reproduce the same binary as bitcoin.org or bitcoincore.org?
The challenge with creating reproducible builds is that you need to ensure that the build process matches exactly across different operating systems and different architectures. Bitcoin uses Gitian, a deterministic build process to achieve that.
Bitcoin Core provides the configuration and build instructions for various operating systems in the /contrib/gitian-descriptors directory in the Bitcoin source code.
For Linux you would use this gitian-linux.yml.