The GP said, "and exponential". If AGI is exponential, then the first one will have a head start advantage that compounds over time. That is going to be hard to overcome.
Nothing is truly exponential for long, but the logistic curve could be big enough to do almost anything if you get imaginative. Without new physics, there are still some places where we can do some amazing things with the equivalent of several trillion dollars of applied R&D, which AGI gets you.
It astounds me that people dont realize how much of this cutting edge science stuff literally does NOT happen overnight, and not even close to that; typically it takes on the order of decades!
My point being that even if Science ends today, we still have a lot more engineering we can benefit from.