Since you want to just position the platform from position A to position B (and I suspect that the motion is horizontal i.e. gravity does not get involved), then the main torque you need to overcome is due to losses on the pulleys.
However, the problem there is that the losses on the pulleys will be depended on many factors:
- load (platform + any weight on it)
- bearings used on the pulley
- correct alignment
- tension on the cable
- type of "cable" (e.g. belt, synchro belt, chain)
The bad thing about the above (with the exception of the first) is that they are very difficult to quantitatively assess.
the good thing is that if there is a proven design and assembly methodology (its deceivingly important), they won't have much an effect.
So bottom line, try to find a cost effective stepper motor with a decent torque (you don't mention sizes but for example most 3d printers use nema 17), and get a stepper motor driver that allows you to adjust the Amps to at least 2 times the nominal amps. Then even if you run into trouble with the nominal amps you can adjust the Amps.
PS: What you are trying to do is essentially load supermarket trolley and push it on a horizontal plane. If the floor is smooth enough and the wheels properly rigid and round then the pushing force to keep it moving is very small (its getting it to move that its the problem).