I'd suggest not worrying about the cassette, practice getting up to speed as fast as you can from stopped.
The only reason to change from an 11-32 wide range cassette is if you find yourself never using the larger sprockets when climbing hills or you find the difference between the gears as you change too much.
As has been said above, other riders are simply better at selecting the right gear for them to get up to speed from a standstill.
Personally i find using the big 50t at the front and a 19t or 21t at the back and spinning the pedals like a lunatic works for me. You need to play with different gears and see what works for you.
If you can pedal at a high cadence (>120rpm) you may find that helps too, as I find it easier to build speed in a low gear and change up.