It is a convention, but there is a reason to prefer this convention to one where you add first, which is that multiplication distributes over addition, but not the other way around:

(1 + 2) x 3 is (1 x 3) + (2 x 3), but 1+ (2 x 3) is not (1 + 2) x (1 + 3).

That means that a lot of expressions where sums and products appear, like polynomials, would require using more parentheses if we were to write in a system that adds first.

Performing products first also keeps things consistent when working with units in equations: 50 meters + 10 meters = 60 meters, "meters" can be seen as a thing that gets multiplied by 50 and 10 and 60. If you added first you'd need parentheses to write that.