In the eternal inflation our universe has the approximate age of 13.7 billion years.the question is; what's the age of the first universe that was made according this theory ?thanks
The simple answer is that no-one knows.
There are some general arguments that eternal inflation must have started a finite time ago i.e. eternal inflation can't have been going on forever. These are described in section 6 of Alan Guth's paper Eternal inflation and its implications, but the arguments are a bit technical and I'm not sure how easy they it would be to present them in a simplified way here.
Anyhow, there is currently no theory to describe when and how eternal inflation got started, so we have no idea when the first bubble universe nucleated.