Are there ways to speed up the growth of plants?
Yes.

The research team, led by the Durham Centre for Crop Improvement Technology, and including experts at the University of Nottingham, Rothamsted Research and the University of Warwick, have discovered that plants have the natural ability to regulate their growth independently of Gibberellin, particularly during times of environmental stress.
They found that plants produce a modifier protein, called SUMO that interacts with the growth repressing proteins.
The researchers believe that by modifying the interaction between the modifier protein and the repressor proteins they can remove the brakes from plant growth, leading to higher yields, even when plants are experiencing stress.[1]

Bacterization is the process by which bacteria applied to the soil and plant parts. Under certain conditions yields were able to increase 10 to 13 percent. However, not all results were able to be reproduced so this is something you can look into more as well. [2]
Another option is to artificial increase the amount of CO$_2$:

Over the years there have been numerous laboratory experiments which conclude that increases levels of CO2 result in increased plant growth no matter how that plant growth is quantified. Sylvan Wittwer in Food, Climate and Carbon Dioxide tabulates the results. [3]

Lastly, you can look into genetically modified organisms (GMOs) which is a hotly debated topic.
With a Google search, you will see that that there are numerous articles on methods to increase plant growth, to numerous for me to give a blurb about them all. Therefore, I linked a few that seems promising as well as interesting.