I've been able to get onto the platform where you wait for the blue platform from the starting area, but unfortunately the blue platform won't activate until you activate the red one. If you could somehow get across the gap over to the other area (right before the red platform) similar to the starting area you could get to the red platform faster, however you still have to go down the elevator at the start and kill the two spiders, otherwise the red platform won't activate when you stand on it.