You have to first acquire the talent, then train them to be NHL athletes. I'd wager that's a 5 year process. So in 6 years, 2 draft classes will have made it (only a percentage).
At that point you start fine tuning your playoff team to try and win a cup. If you did a good job, eventually you win it. 12 teams have won the cup going back to 2000, 6 have a single championship in that time. So, in 21 years, 6 teams have won 2.67 cups. Those are tough odds and it's likely a big reason why you see good teams retool if they have some quality youth.
I'm not happy about the proposed timeline, but IF we win a cup, I don't think it will be a short road.
I wouldn't say I'm giving the GM 6 years to be a bubble team, though that could be the case depending on how quickly guys progress. I'm giving a GM 12 years to win a cup, or at least look like their team could, because actually winning a championship is hard.