Yup, indeed, the fastest way, in 2-4 h you can go from rank 0 to the rank you need to get the Vette - as a side note, I advise you o use a T9, or at least a T7, or a Python, in case you do not have an Annie - AND to fit a lass 1 or 2 collector, and 7-12 limpets - all the utility slots fill with heat sinks.If you want to rapidly increase your standing with the Feds, outfit a ship with as many Economy Class cabins as it can hold and start evacuating passengers from burning stations when you see them. Use Inara to find the station with Federation factions and pick up the passengers from them. Deliver them to the rescue ship right outside the station, rinse and repeat. By far the fastest way to pick up rank for either of the superpowers.
You will double the points you need to get the rank if you do the trip with passengers AND you collect the escape pods, correspondence, black boxes, etc - each item you collect will give you rewards in reputation at the station you drop the passengers you saved, under the tab "missions" ( do NOT give the items at "rescued" but instead selection the missions for the factions you need ( empire or federation) for those items you harvested from the burning station.
Like that, you will get x 2 reputation points - both from passengers AND the missions rewards. For ex. 3 black boxes or 3 escape pods can give you the same reputation points as saving 25 peoples. Better to get both at once, in one trip. Time-saving grind