You can achieve a roughly 200 turn (standard speed) Contact victory without relying on Progenitor Ruin RNG.

Two requirements:

• Play as Slavs or Franco-Iberia (due to slingshot possibilities). Slavs are luck-based (getting a satellite from a ruin so you don't have to actually build one but a Miasmic Repulsor is easy enough to tech/build for anyway) and F-I is time-gated (hitting Mechatronics before 10th Virtue). I believe F-I is a bit stronger since luck isn't a factor and you don't have to sit on satellites that you might find.
• Have Titanium, Firaxite, Petroleum resources (needed for Deep Space Telescope). We'll pick up all techs necessary to gather each resource in this strat. Remember that you can trade for these as well.

Overall Strategy:

• This game is built to be played wide/ICS for optimal play. Hammers are extremely important for this VC due to needing to build 1) Deep Space Telescope, 2) Transcendental Equation, 3) Decode Signal, 4) Contact Beacon. They all cost a crapload of hammers and since trade routes scale with number of cities, you want as many trade routes going into your capital as possible.
• Tech speed isn't all that important (edit: It will dictate overall finish time -- the quicker you hit Mechatronics, the faster your overall win time will be). The only requirement is, if you're playing as F-I, to hit Mechatronics tech before your 10th Virtue. It's easier than it sounds. Once you've researched Mechatronics, the only other techs that you'll need is Bionics, Computing and Transcendental Math. You can literally pick up no other techs and still win (quickly).
• Virtue and Virtue order doesn't really matter. What matters is hitting 10 Virtues on or after you research Mechatronics as F-I. Use the T1 width bonus to pick up an extra Virtue. Personally, I go with a mix of Prosperity and Knowledge but Industry is really good too. The health from Prosperity is good but not as important to this strat since we pick up Bionics (which means Biowells). Edit - Just found out in my current game that the 1st Industry Virtue ( 10% towards buildings) works on all the crap we have to build (Signal Decode, etc.). Looks like taking 2 into Industry for that and 15% towards Wonders is well worth it.
• No Affinity requirement (you can finish a Contact Victory with 0 Affinity points). Choose what you prefer.

Step-by-step strategy:

• Loadout recommendations: Artists. It's, IMO, the best for any VC, any civ. Everything else can be tailored to what you prefer.
• Landing: Try to land on coast. 50% yield from trade routes.
• Tech: Pioneering
• Build: Old Earth Relic (OER) > Explorer > Explorer. Try to explore coastline so you can establish naval routes ASAP.
• Tech: Chemistry/Ecology/Genetics (Ecology can be skipped if there's 0 Aliens to mess with your trade routes). Genetics is great for the science and health boost.
• Build: Trade Depot, Trade Vessels/Convoys, Colonists x infinity. Feel free to tank your health because health doesn't matter if you choose to ignore it.
• Satellite city build order: OER, Research Lab, any science buildings, any health buildings, or you can even build Culture. Build Vessels/Convoys as needed to max route capacity.
• Tech: Engineering > Robotics > Mechatronics (should be completed roughly turn 100-120)
• If you're Slavs, launch satellite after you hit Mechatronics to get Astrodynamics. If you're F-I, use your free tech on that OR Orbital Automation (Astrodynamics leaf tech that lets you build Deep Space Telescope).
• Build: Autoplants
• Tech: Bionics
• Build: Institute (in capital only, don't need it anywhere else). You'll also have Biowells ( 2 food, 1 health) so you can just spam those everywhere to get out of unhealthiness. I typically spam Biowells in the capital and Generator spam in satellite cities (to maximize food and hammer differential).
• When you get the Institute quest, spend the free tech on either Astrodynamics or Orbital Automation (whichever you didn't pick up from your UA).
• Build: Deep Space Telescope, launch over capital.
• Tech: Computing > Transcendental Math
• Build: Transcendental Equation
• Between the time you've launched your Deep Space Telescope and finishing the Transcendental Equation, you should have made 1 out of 2 contact requirements from the Telescope. Finishing the Equation will give you the 2nd and unlock the Decoder.
• Build: Signal Decoder
• Build: The Beacon (roughly turn 150-180ish)
• Before you begin powering up your beacon, sell all your energy per turn for lump sum from your buddies so you can have a huge stockpile of cash in case you need to spam defenses.
• Power up the beacon

And that's pretty much it. For your satellite cities, all you really need are Trade Depots, Autoplants, culture and science buildings. I usually switch to spamming Colonists or Culture when there's nothing else to build.

Some folks have reported sub-200 turn CVs. If you get REALLY lucky with a Progenitor Ruin, you might even be able to win at 150 or lower! Getting 1 Contact requirement from a ruin means you can skip the ENTIRE Deep Space Telescope part and go straight for Transcendental Math/Equation. The hammer cost for Equation/Decode/Beacon is still going to be a big speed bump.

edit 2 - Game I just finished: Turn 202 Contact Victory http://i.imgur.com/TQKDiJA.jpg (deleted all external trade routes after I started powering up the Beacon)

edit - Thank you kind stranger for the gold. <3