Do I understand correctly, you want to open an application and have it NOT be the active window (ie default WIndows OS behavior)?
if possible, I'd look at command line start up options as the most likely simple method. HOWEVER, that is using OBS in an odd manner (unless you are using some other control interface). OBS is the tool to composite a video. It is designed to be interacted with. So for default/basic OBS, starting in background makes no sense to me.. Now, if you are gaming and using something like stream deck, then it makes a little more sense (but even then, I have a hard time thinking of a scenario where starting OBS normally and default OS behavior of it then being the Active Window would be an issue)