Does our Sun have a great-grandmother?

[matt-browne-sfw]

We all know that our Sun is made up of material ejected from a supernova. For the sake of illustration, I'd like to use the picture of a "mother" here. Well, not only our Sun, the Earth, and we all "children" of an ancient star ending its life in a supernova, and its material later giving "birth" to a new star, and even planets in this case.

Because our Sun is metal-rich, this cycle must've happened twice. So, there's a grandmother in the even more distant past.

I'm unclear how far the research has gone by now. Is the grandmother a child of the big bang? Or is there yet another previous giant star ending its life as a supernova? Do we have a chance to ever find out? Can the grade of metal-richness (stuff heavier than helium) be a precise indicator? Can simulations of nebula / interstellar clouds tell us about the timespan between the supernova and the ignition of the nuclear fire of a newborn star help here? In short: How many supernovas after the big bang?