Maybe impossible. Took more than 30 minutes to get a secured area. Very small map, and I got crap for starting area because the digitalis has the high ground.
Took about 20 minutes to get a foothold and just over 30 for me to beat it outright, so I'd bet those 20 minute scores are valid. There's enough ground to grab and build out slowly at the beginning, as long as you manage your energy carefully. I had to use the one conversion to give me a little more time early on to build out the base with minimal weapons/energy.
It's possible - JB, 15 min :P
You have to concentrate on the smallest defensible space w/ 2 Pulse Cannons, one just above the 5 wide divot and one towards the bottom Totem. Then asap towards the end of those building put a mortar next to the bottom one, you'll barely have a foothold but on the bottom towards that totem, and next a mortar on the landing zone to the north/and a pulse cannon to prevent the creeper from wrapping around. I ended up moving my 3rd pulse cannon to the east side of the landing zone so then I had 3 pulse cannons defending my land, and that was very stable. You won't be able to get the totem and a forge going until you have ~3 mortars and ~4 pulse cannons or so. Build ~5+ reactors and at least 1 terp to make land usable before a forge. Focus on energy and minimum mortar/pulse till energy 2, and you only need to deal with 1 spore from the tower so you can lazily build 2 beams when that hits 1:30 or less.
It takes a couple tries to pin the start, focusing on getting the most efficient collectors and the first 2 pulse cannons + mortar. It was critical for me at least to put the top pulse cannon up first, and then a couple seconds/build cycles later plop out the second pulse cannon. I deleted 3 or so collectors after I was >10 reactors to get more efficient land use while it mattered, and I only got up to 4 Bertha's.