Well it does sound like a silly question but it's not really. Every new musician goes through the same thing.. you're waiting for "aha!" moments. I have no idea why the person said 2 months. These "break through" moments are just moments where you go "aha! so that's how it works!".. and your playing improves automatically from it. It's not something you can really put a time on unless you are studying music at college or something like that.. and even then it's still a matter of you personally understanding the "break through".

May be the person who told you that had a breakthrough themselves at around 2 months after playing.. that doesn't necessarily mean you will also have a revelation at the same point.. or even the same revelation for that matter. That's all this is about really.. There are lots of little breakthroughs along the way of course.. like the simple act of strumming down AND up... at first, a lot of people find this difficult.. once they get over the awkwardness they have a sort of breakthrough moment. Being able to strum up and down opens up a whole world of rhythmic opportunities that weren't accessible before.

Having a "breakthrough" moment doesn't end a particular avenue of learning.. it just opens it up wider.