Check out some of the plots here https://en.wikipedia.org/wiki/Technological_singularity

Though many events are cherry picked, the trend is still quite a nice fit it seems. I would say exponential growth is rather plausible.

In fact it doesn't even need to take aliens to change our timeline. In Cosmos by Carl Sagan he often talks about so and so Greek guy that was basically correct but dismissed. They had some inkling of the experimental method but didn't pursue it. They knew about the motive powers of steam. They just didn't think much more of it I guess.