I presume this is more about the direction Firefox is going in, but I also think more people would have noticed, so I'm trying to get more information. All you need to do to help with this is disconnect from your LAN and start Firefox-- if you have it installed.
Based on what I've tried, I think this is less about the computer connection to the LAN and more about the connection from the LAN to the internet. So just plugging into an otherwise unconnected router wouldn't change this.
Basically, if I'm connected to the internet then it takes 15-30 seconds for Firefox to start. I'm not at all concerned about that. If there is no internet connection, it can take a minute or more. This difference does not change if it's the first thing I do when I start OpenBSD. It does not change on a second try so I'm ruling out any sort of caching issue.
I don't know if this happens on other operating systems, such as GNU/Linux-- right now I don't know if this even happens on NetBSD at all. If this is only happening on OpenBSD then of course I would suspect Pledge (I'm a fan of Pledge) but I'd love to know if this happens to anybody else on either OpenBSD or NetBSD. I am not trying to fix it, only to determine the breadth of the issue. I am curious if Firefox is at fault. If Pledge is responsible and NetBSD is not affected, then I am unconcerned about it.
Since discovering this with default settings, I have searched for various things I can turn off to make the browser load faster-- again, not to fix this, Firefox loads quickly enough for me-- I am trying to learn what does this. I have not found anything I can turn off to get it to stop behaving this way.