How long would it take to travel from Tian-Xia to Avistan using mundane methods? Is it even possible to do so?
Yes, it is possible. But distance and time are unclear
There is one ship notorious for doing a lucrative trade route between Tian Xia and the Inner Sea region: Hu-Hazhong. It is described in detail in the Ships of the Inner Sea campaign setting book, but there are no mentions on how long those travels take them.
Hailing from distant Tian Xia, the junk Hu-Hazhong has traveled to the Inner Sea in the hopes of trading exotic fare from the Dragon Empires for goods from Avistan and Garund that hold much value in the east.
But also adds this when describing the ship:
Ever since the Resplendent Phoenix first arrived in Absalom some 3,000 years ago, the people of the Inner Sea have been fascinated with the strange and wondrous goods produced in the far-off Dragon Empires of Tian Xia. The first glimpse of a Tian junk in the distance thrills merchants, their wealthy clients, and pirates alike, for all know that when those distinctive sails appear on the horizon, fine silks, exotic spices, and untold treasures are sure to follow. The Hu-Hazhong may deliver all these things and more, provided it can survive its arduous journey.
And the book also describes how dangerous the journey is:
The journey was more difficult than either could have imagined, yet Narava’s guidance from her past lives has carried them through. Though the ship has suffered casualties—eight crew members in all—it has successfully navigated its way to the Inner Sea (...).
Tian Xia is two oceans away from the Inner Sea region (Garundi and Avistan). Ships have to cross the Embaral Ocean, which is described as the small ocean separating Tian Xia and Casmaron, and then the Obari Ocean, which separates Casmaron and Garund.
You will notice that the Obari Ocean is described as having several trade ships going from Vudra and even from Tian Xia's city of Goka:
Trade via ships is common along the coastlines bordering the Obari Ocean, with vessels from distant Vudra being the most common, although occasionally even ships from distant Goka on the continent of Tian Xia are spotted.
Aquatic Adventures makes mentions of ships leaving one continent and "disappearing" for months, which raised suspicions about the fate of their crew. So, I suspect that long journeys should take at least a few months, with shorter journeys taking a few weeks.
The Ruins of Azlanti adventure path also mentions that a ship took six weeks to travel from Andoran (in Avistan) to a not very well-localized archipelago in the Arcadian Ocean, in the opposite direction.
After six long weeks, this morning the crew of the Peregrine sighted land to the west.
But considering that the archipelago in the adventure is located near the ruins of ancient Azlant, we can guess that it is located about a thousand miles away from the coast of Avistan:
A thousand miles off the coast of Avistan lies a labyrinth of shoals, steep cliffs, and islands, remnants of the long-destroyed continent and island nation of Azlant.
I would say that such travel would be at least a thousand miles away, based on all that information.
Perhaps the least populated of Golarion's continents, the Crown of the World1 is certainly not the least traveled. Covered in glacial ice, the landmass sits atop the world and serves as a passage from Tian Xia to Avistan, the most well-known of which is called the Path of Aganhei. Traders and explorers frequently brave the harsh cold to reach the other side of the world via this shortest route.
But that is a hard travel due to the harshness of the terrain, it being not well charted outside of the route and the incredible danger of the region. But we live in a world with magic, so that would depend on their level and how well equipped they are to survive in frozen wastelands for a while. However, if this did take more than a few weeks (or a month), I would think this wouldn't be a good trade route, as people would likely perish in the voyage before they could sell their goods at the other side, forcing them to take safer routes.
To contrast ShadowKras's great answer for mundane travel, a commoner could travel almost instantly between the two.
If the commoner is within or near a Large City or Metropolis they can hire a spellcaster to cast Greater Teleport for them at a cost of caster level (varies from 13-16, depending on the casters list) * spell level (varies from 5-7, depending on the casters list) * 10 for a total cost from 650-960gp.
This may seem like a lot, however there are a couple different points to note about it.
- Greater teleport allows for the caster to teleport another medium creature for every 3 caster levels they have. This allows the caster to bring at minimum 4 different creatures when they teleport. These creatures could then split the costs for the teleport amongst themselves, reducing the costs to about 165-230gp each.
- This cost also has to be compared to the cost of mundane travel for the trip, which includes rations, any animals or wagons used, the cost of inns, and the cost of passage fares. Additionally, given the far distance, there is the risk of bandits or other encounters when travelling in a mundane manner, which adds additional cost in the form of guards or other equipment designed to help the commoner fend for themself.
- There's also the obvious factor of time difference in arrival between the two methods. Mundane travel takes a long period of time to arrive, while teleportation is near instant. This could allow for fluctuations in the value of any trades the commoner may have sought to do when they arrived.
Another magical alternative is the usage of scrolls of Greater Teleport, which may be found in settlements the size of Large Towns or bigger. This has the disadvantage of a higher cost (1,625-2,400gp, depending on the creator), and the necessity of a UMD check. However, it does allow for a group of commoners to bring one more, as one person is the caster using the scroll.
Alternatively, a merchant group may have set up a permanent Teleportation Circle between cities on each continent. This has a steep investment of 23,500gp (or 47,000gp for circles both ways), but the merchant group can slowly recoup this cost with profit made from trading, and fees to use the circle for easy travel to others who are not a part of their group. In all likelihood, the cost for a commoner to use the circle would range from 150-250gp as that would be a competitive price with hiring a spellcaster to cast greater teleport.