Hi everyone. 
Before people complain about the question in the title, let me explain: I don't have LBP 1, I have no idea of how to create a level, and I have only played the first 3 stages of story mode. 

Recently, I was trying to create a level, but couldn't found the menu option. I think I searched everywhere but still no "new level" option on sight. 

Is there some condition I have to fullfil to access that option (like when they make me play the entire Da Vinci stage in order to unlock the "Community" menu)? Or I am just not looking at the right place?

Go to "Me" on the right, then go to your moon, and select a crater, and keep hitting X until you get into create mode.  
 
However, you should go through the tutorials first. 

And yes, you have to play the first section of single player first. After that they will show you where to create.

Also it's advised that you finish story first, you get a lot more things to use in your level. Also do all the tutorials. It may seem like there's a lot, but it flies right past with Stephens voice.

Also good to know, if you want to pause the vid in the tutorial, press Start and then X to pause the vid

I second the advice to play through single player first.  You get A LOT of new items that way.