Anime wasn't always considered Anime, it was Japanese Animation or Japanimation until in the mid-to-late 90s. The term "anime" is essentially the shortened version of it all so techncially anything that is animated, even CGI movies are considered anime, yes even Shrek.

With that said, american cartoons are also considered anime in Japan. From a Japanese point-of-view, any animation is considered Anime and therefore cartoons are anime. However, this is not to say that in the US or outside of Japan this isn't the case. Anime is generally referred to as Japanese animation and not just any kind of cartoon or animation.

Where am I going with this you may ask? It's to answer your question because there are two types of Anime. The anime you hear people talk about in Japan and the anime the non-Japanese talk about. The very first anime happened in 1917 but wasn't called "anime" at the time. I wrote an article decribing how anime actually comes from a french manga artist but basically it did in the 1970s. The term gained momentum especially in the 80s. In the 90s that's when it became very mainstream and in the mid-to-late 90s it was all over the world.

Unfortunately there was an anime crash in the 90s but the industry bounced back. It might actually happen again but we will see if it does or doesn't.

I'm not sure in which article the details of this information is in and it may have been hidden at some point. Here's a list of articles that may be helpful: https://www.jappleng.com/education/course/overview/4/japanese-culture