Windows XP had an obvious folder in the Start menu called "Startup". You could put anything you want in there, and it would run when Windows starts.
That folder still exists (at least in Windows 10 it does, I've not used 11 at all), but it's not in the Start menu anymore and you have to go digging through the filesystem for it. I've forgotten exactly where it is, and I don't have a Windows rig at the moment to explore either. But maybe the knowledge that it exists will get you going?
If you've already solved that part, and you're asking instead about OBS just sitting there when it starts and not automatically streaming, you can modify the shortcut, or line in the script, or however you start it automatically, with some command-line flags. Run obs --help
in the Command Prompt to see all that you can do there.