> "Infinite" exponential growth at the scale of the universe might be possible
Only if the speed of light turns out not to be the hard boundary that it appears to be as of now.
If humanity is bound by any maximum speed (e.g. c, the speed of light), the maximum accessible volume of space is a sphere with radius c * t, where t is the time spent exploring the universe. The volume of this sphere is O(t^3), which is very much not exponential.
That being said... we do know that infinite exponential growth of an economy in a finite bounded space is not possible. Eventually it must either plateau or crash. We hope it plateaus. There are some positive signs in this area including most notably the decline of birth rates with development but there is no guarantee those trends will not reverse.
"Infinite" exponential growth at the scale of the universe might be possible, but the distances between even planets (e.g. Earth and Mars) make separate economies at that scale more or less separate systems. We could colonize Mars and continue growth there until that either crashes or plateaus, but that would not impact the growth model of Earth very much.