God, I hate being the math nerd.
But, I'm going to be the math nerd.
At 1,000 cobble a second (which is possible) you can produce just about 90 million cobble a day. Call it 100 million for ease of math. A billion would take 10 days. A trillion would take 10,000 days. Or, roughly, 30 ish years. Upping your cobble to 100,000 a second (which I'm not sure is possible) would drop that to 3 or 4 months. Realistically, it would be somewhere between those two extremes. Say 5 years or so. Of your computer running Minecraft 24/7.
I mean, if that is your thing, have fun.
(hmm, I do wonder what is the max speed you can produce cobble. Igneous extruder is probably the best way, I just wonder how many you could have going at once before you either overload the pipe system and/or your computer)