In general, the kernel starts one program after it finishes booting, and that process starts everything else; traditionally it’s called ‘init’. systemd is a “modern” replacement.

Different distributions and unix variants use different “init” patterns and tooling; so find out what your distribution is using.

Those patterns are designed for this use case but you need to understand the different phases of startup and where your script should fit in.

What distro are you using?