How long after baking do American chewy cookies get their normal texture? I just baked my first ever batch of American-style cookies (chewy chocolate chip cookies). I used the correct ingredients, including actual wet brown sugar, except for the chocolate - I had no chocolate chips, so I used chopped milk chocolate (I know, I know...). 

I have experienced this type of cookies as a light, but not soft baked good. When I have had them, they have been slightly airy, but more tough than brittle. I suppose that this is the desired texture, as they are called "chewy". 

I took my first batch out of the oven, and it seems that I reached too deep with the glove and touched a cookie. It was squished. All the cookies turned out to be puffy and prone to deflating. Also, they have a cracked surface, unlike the pictures in the recipe illustrations. 

Is this normal? Will they get their expected texture later? How much will I have to wait for them to get the desired texture? Or did I make a mistake? 

I didn't cool the dough, although I have read often that cookie dough should be kept cold. The reason is that this recipe directed me to melt the butter, and didn't include cooling steps, so I assumed that a warm dough is normal for the recipe.
The cookies will set (take on their final texture) about by 20 - 30 minutes out of the oven.  Coming directly out of the oven, cookies will absolutely be soft and squishable; which is why you should wait a few minutes before moving them off the baking sheet and onto a cooling rack (you can cheat this time if your cookies are all on a sheet of parchment paper, and you move the parchment paper as a whole).