Was the universe already expanding before inflation occured? Was the universe already expanding before inflation occured or did inflation cause the universe to start off expanding?
By “cause it to start off expanding” , I mean the cause of the initial expansion.
 A: 
Was the universe already expanding before inflation occured  or did inflation cause the universe to start off expanding?

It's not possible for the universe to be in a non-expanding phase and then enter an inflationary phase.
The idea of cosmological expansion is based on two pieces of evidence, one theoretical and one observational. Observationally, Hubble et al. observed the Hubble law. Theoretically, it's not possible to construct a static cosmology in general relativity without fine-tuning.
For the very early universe, we have little clear observational evidence, but the theoretical argument still holds.
All of this is on much more solid ground than anything having to do with the inflation hypothesis. We actually don't know whether inflation is right or not, although it is a very popular idea among theorists.
It's a popular misconception that inflation caused expansion, is needed in order to explain expansion, or is the same thing as expansion. It's not.
A: Here is a link discussing  cosmological models, as one has to keep in mind that the models develop in order to fit/explain observations using current physics theories, classical and quantum mechanical.
The current mainstream model can be seen here, and your question is about what happens at the quantum era, before $10^{-32}$ seconds.
Here is an image of the current mainstream chronology that includes the current models for that time:

Between the fuzzy ball that has replaced the classical singularity and to the end of inflation at $10^{-32}$ seconds, quantum gravity reigns, and quantum gravity is still an open problem.
The above current model assumes a period before inflation starts, where the inflation is very small. The inflation period starts later than the fuzzy beginning of universe, and is

Triggered by the symmetry breaking that separates off the strong force, models suggest an extraordinary inflationary phase in the era $10^{-36}$ seconds to $10^{-32}$ seconds. More expansion is presumed to have occurred in this instant than in the entire period ( 14 billion years?) since. 


So the answer is that in the mainstream cosmological model  the universe is expanding after the fuzzy beginning at a very low rate, and suddenly inflation sets in because the temperature has dropped to the symmetry breaking between strong and electroweak forces.
Keep in mind that cosmology is an active field of research, and we are discussing here the current mainstream model.
