I'm a homebrewer now...

The beer is done when it's done. Any "hard target" is bad advice.

Generally, in a proper fermentation the beer is ready in 7-10 days. But it may take longer, longer than 3 weeks even. And if you're a new brewer and your fermentation management isn't up to snuff then it can take longer than that.

I've had beer completely ready after only 5 days.

There's often no harm to leaving beer longer (within reason), but no harm does not mean there's necessarily a benefit.

 

So after eight days in the bottle (I'm sure that it could be left longer here, too ) I decided to chill one down and give it a try. I was fearful of bottle bombs, and equally worried that they wouldn't be carbonated at all.
There was a resounding pop when I flipped the wire top, so my worries about not carbing at all seemed wasted. Lots of sediment because I didn't let it sit long enough to clear before bottling, but I understood that would happen. Nice creamy head from a careful pour. About this time my wife wandered in to see what the popping noise had been and said "hmmm that smells good" as I was rinsing out the bottle. She tried it and said it tasted good but was a little light for her. I tasted and thought it was pretty damned tasty, but definitely would be better if I hadn't rushed things.
So lessons learned, I have some decent brew from my first ever batch to drink up. And then I'll be ready to try another kit or perhaps even a recipe from here. Maybe another kit first to build a wee bit more confidence first.

Thanks everyone for the guidance.