After a few hundred resets, i finally got the 3:05... and forgot to record the sound. So i decided to do it again and got it within an hour - lucky me.

3:04 is possible, although grindy. At this point, you already need your factory to be insanely lucky, like 1% or less. I don't think there's a full second to gain in pathing in Ski and Space. Good luck if you want to try!

Played on BGB Emulator, recorded with OBS and cut with Shotcut.