The fastest you can get speed is with a 1 second extractor. This is the fastest Zerglings you can get. Writeup and build from of Wizecrax
https://www.reddit.com/r/starcraft/comments/35ysu9/this_zvzzvt_legacy_of_the_void_build_order_is/
Why is there no SALT encoding or Overwolf build?
12 | 0:01 | Extractor | |
11 | Spawning Pool | ||
10 | Drone | Put 3 Drones into gas | |
11 | Overlord | ||
11 | Metabolic Boost | ||
11 | Zergling x6 | ||
14 | Zergling x2 | Pull Drones from gas | |
15 | Queen | Drone up until full mineral saturation on 1 base and DOUBLE EXPAND |
From Wizecrax
Use your zerglings to harass, kill as many workers as you can and simply be a total pain in the ass while droning up as much as possible until you scout a reason otherwise.. The speed will be so early due to the 0:01 extractor and I have caught even early gas opposition completely off guard.
From this point treat it as a 3 hatch opener with Speed and branch out into lair tech as you see fit.
I have done this build order against every race since it is my go-to vs random. Ironically against Protoss it has done the worst (but it has only been a few ZvR games that ended up being ZvP.)
I know most people hate 1 base openers or cheese of any kind but a Win is a Win is a Win...