First, let me refer you to this thread, since I have not yet achieved a science victory before turn 250.
https://forums.civfanatics.com/threads/civ-6-sub-t300-science.675666/
Next, let's assume that you're playing GS or later, so that 4 parts of the science victory are needed: Satellite, Moon, Mars, Exoplanet Expedition. Each of these parts must be done sequentially, with the last 3 parts requiring techs to be researched after you've built your first Spaceport. Yes, use builders with Royal Society to speed up individual projects, including the lasers to speed up Exoplanet once it is launched. I'm not sure when the Royal Society is unlocked, so I'm not sure if you can use it to speed up Moon Landing. But five spaceport cities won't help get through the first 3-4 parts faster, since they are sequential. Looking at the finish,where you're building multiple laser stations to get to 21 light years per turn, that rate also has a ramp up. Your ship will start out a 1 LY/turn, then 5, then more, as you rush to complete the additional projects. Total turns for *travel*, after launch, may still be 5-6.
Great Scientists can be used to speed up Moon Landing and Mars, more rapidly than expending builders.
My short answer is to look at each segment in the chain, to compress its timing, so that you can perhaps complete all 4 steps in fewer turns.