Hrmm... Okay, let me think...
Assuming The Wyrm Ouroboros' time frame is correct, that still leaves the corps with a small but significant window in which to try and deal with the Levithan, and adjust before the world collapses. I think a lot of people forget exactly how quickly humanity can adapt their technology to deal with new things when they are sufficiently motivated (and total planetary meltdown would probably be sufficient motivation).
So, the first thing the Corps are going to do is try and determine the actual capacities of the creature. Knowing it's abilities is going to be key to living with it if they have to, and destroying it if they can.
First Thought: It probably isn't capable of moving on land at all at the size we're talking about... doing so would likely kill it due to it being crushed under it's own weight, and even if not, the speed of movement we're discussing in the water would imply a method of propulsion that was extremely well suited to it's environment (probably akin to the jet propulsion that squid use), and therefore not at all well suited to movement on dry land (which is to say the bearing of weight and navigating of difficult terrain). Corps are probably going to assume that the Godzilla scenario is out of the question because of this, and at least try the coastal shipping... and as Wyrm pointed out, most of the cities in the sixth world are going to be desperate. SOMEONE is going to try coastal shipping (or be used by someone else to try it) despite the risks, because the eventual result of not having tried it is, bluntly, far worse than the destruction of a single city.
Corollary: The creature probably also has a given set of physical characteristics that will limit its activities even in it's natural environment. Shallow water, for instance, may prevent it coming close because it would lack sufficient space to move. Similarly so with narrow but deep water (canals and the like). These possibilities will be vigorously tested, because the loss of ships and crews in testing them frankly would mean nothing to the human race (or the corps), in the face of total extinction.
Second Thought: How is the creature killing these ships and airplanes? Ships, okay, that's easy, it sinks them. Pulls them under the water and crushes them or breaks them apart as you choose. Conveniently this answers submarines as a question as well (it pulls them down below the crush depth or breaks their hull and they flood). It is the planes question that is really important, because the means by which they are destroyed suggests possible counter measures to the creature. Does the crew simply die and the plane crash? Okay, you're going to see unmanned planes pioneered in record times. Are they physically knocked out of the sky (seems unlikely, due to size concerns. Remember that most planes fly at an excess of 15,000 feet in the air, which is slightly more than four kilometers up). No, it seems likely that the only way those planes are being knocked out of the upper atmosphere is via magic or misdirection. Also, don't discount the stratospheric zeppelins. They're faster than boats are, even while having slightly longer routes, and while they can't carry as much as a supertanker or supercargo ship, they can still carry quite a lot of weight (comparison: most modern cargo ships travel at about 23 knots -about 26 mph- while zeppelins and other airships historically averaged out at somewhere between 60 and 80 mph).
Third Thought: You mentioned that Leviathan was asleep, and the ritual specifically woke him up. Does the ritual need to remain active for him to remain awake? If so, you can imagine that the corps might just be willing to glass an entire city if they had reason to suspect some of the Ecoterroists who were maintaining it happened to be there... just to be sure. Because when you can tell the rest of metahumanity that you had to do it or they and their children would have starved to death in the near future, you can get forgiven for quite a lot. In Shadowrun history, see Chicago and the reaction to the bug threat for an excellent example. Even runners who typically get all contrary about corporate actions on general principle, don't usually disagree with what was done to contain and destroy the insect spirits there.
If the ritual doesn't need to remain active for it to remain awake, you need to consider what actually made it sleep before, and what it needs to remain awake now. You called it a proto-horror, so presuming it functions on the same rules as the other horrors in the setting, it needs a certain amount of ambient mana to remain active. Are we at that stage in the world yet? Will we remain there if vast swathes of metahumanity starve to death? Is there a counter ritual that might force it to sleep again? Heck, what about a Great Ghost Dance to deal with it? Or can the Great Dragons and Immortal Elves (who might very well remember this thing from the past) put together a ritual to stop or slow it? All of these things are going to occur to various people in world.
Fourth Thought: Nanotechnology and biotech weapons. Sure, the thing may have shrugged off a nuke, but you're not just going to give up and stop there. In the world of Shadowrun, nukes are not the be all and end all of all weapons tech. Someone out there is going to try deploying weaponized nanites into the 'god' to track or destroy it. Someone else is going to consider trying a counter hostage attempt on the Ecoterrorists, releasing a bioweapon that will eradicate all sea life if they don't let at least some shipping get through (or tailoring one to try and attack the leviathan if they're a bit more reasonable). Remember, you've made the people of the world desperate, and any one can tell you that desperate people are dangerous.
Fifth Thought: Most cargo is transported by sea because it is efficient. A relatively small investment to create the ship, combined with minimal maintenance and crew requirements, can transport a lot of goods in each voyage for a lot of voyages (generally expected to have a lifespan of 25 years). In Shadowrun this is made worse by mana wastes and radiation on land complicating travel, but there's no reason other means of transit couldn't be used to at least keep people alive (Europe, Africa, and Asia, for instance, could be connected by rail and road networks for transportation, as could North, Central, and South America). Previous experiments with magical and mechanical teleportation may have failed, but was it because the theory is absolutely impossible, or simply because people weren't motivated enough to take risks? People being desperate, both theories are going to be revisited and reattempted.
Ultimately, looking at those thoughts, I don't know that Wyrm was right. Six months to a year before complete collapse might be right, if nothing changed. But this is Shadowrun, where there are computers capable of producing those numbers and being trusted, and also seeing potential solutions. Some corp is going to guess at that time frame and set up a computer program to run through potential variations and solutions at high speed. There are options available that could, with sufficient prioritizing and allowing places to become more self-sufficient, keep things limping along for years. Which gives everyone years to come up with solutions and try them.
And if you aren't willing to go with any or that, or the players screw the world even more? There's always the reseeding adventure, where the players are deployed from one of the orbitals or the Mars base, trying to get back in touch with Earth, and they come back to a world with very few still surviving meta-human settlements.
