Puzzle from yusupov,s build up your chess 1 with not so basic solution. How to approach?

The theme of the puzzle as mentioned in the solution is Greco's mate from chapter 2 example 7(Build up your chess 1).

White to move first

First of all I failed to understand the the method involved in solving puzzles from this book. Of all the puzzles I solved from other books or online, there usually is one unique solution that leads to winning position in the fewest moves. But in case of puzzles from this book I encounter many puzzles where there is no obvious first move .How many moves deep do I need to calculate to find the winning position?

Here in this puzzle one point is awarded after the move 1. Now the question arises why would white move the 1.Ng5 and how does it forces the black to move 1...o-o .Either  I fail to understand the logic behind this puzzle or I failed to understand the criteria for approaching the puzzles involved in this book. 

Am I limited to only the moves that corresponds to the chapter from which I solve the puzzle?

If any of you bright minds can give me an insight about this book and the puzzles, it would be more than helpful.

Thanks in advance

Nope. It's white to move . The solution as mentioned in the book is also given above. My doubt is why would white move Ng5? It could have castled, moved Nd5 or Bg5 etc. How would someone come to the conclusion to move Ng5?

I was working on this puzzle and came up with the idea of playing Ng5, followed by bringing the queen into play. I also noticed that the bishop on c7 was targeting f7. From there, I started moving pieces on the board to search for a checkmate, but it led to such a long line with so many possible variations to consider.

Is finding the Kg4 move enough? I can’t imagine having to calculate the entire variation. The book says Kg4 is worth 1 point, so that’s sufficient, right?

By the way, this is a 1-star puzzle, the easiest difficulty...