I don’t know what the issue is, but it isn’t power, or wake up time. I have a battery powered unit, shown above making the video, and it is almost instant, even first thing in the morning, after being inactive all night. My set-up for this camera isn’t even connected directly to the primary router, but to an extender, so if I did have hiccups, I’d have been looking at that first, but I don’t.
I’ve posted the video above, or a similar one, a number of times, because it is an ideal installation to demonstrate the wake up time. Every single video I get starts here, within half to one stride of having come into view. The wall and bush, particularly the wall, makes it impossible for the camera to have had advance warning and have been ‘waking’ up slowly. They simply come into view, it wakes up, almost instantly, and records. If yours does not, then something else, other than wake up time is going on, because mine does this every single time.
If I had a situation where it took three seconds, pretty much they would be turning away from the door, it would be useless, as others have said, and if this were the case I would be calling support to find out what was wrong.
Post a video of one of your failed/nearly recordings, and I bet someone in the forum can give you some reasonable advice as to what might be going on.