I'm curious : I can imagine that they could build the boat, find the good path, store food or find it on the way, but do you know how they could bring enough water and keep it fresh ?

@Tyrabel There is more in-depth information about the trip. They had bamboo to carry water, and they collected water from rain during the trip. It was shown that ancient methods of storing potable water using bamboo tubes worked.

And, Kon-Tiki benefited from the enormous depth of maritime experience available to Heyerdahl and his crew. @Green's protagonists have nothing of the kind.

@Green So, essentially, "Prove that a non-expert can learn to build a raft similar to the Kon-Tiki expedition in 5 years." Honestly, it never occurred to me that specific expertise was required to strap some lumber together. You can certainly fell trees without a blacksmith, carpenter, or shipwright. You can strap them together without those people and their tools. If you have 20-50 people working on this you can probably launch a few rafts a year for simple testing to prove out ideas and avoid simple mistakes. Given that people did spread to every continent, I'd say it must be possible.

I suspect that reading the books and research resulting from the Kon-Tiki, though, would answer all these questions, since that was the purpose - how could people travel across the ocean at that time. They would surely have explanations as to why they felt that the expedition still proves the point even though they used some modern methods. I'd also suggest that the Book of Mormon has the (short, low on detail) story of an inexperienced group building and sailing such a boat as well, but under the guidance of God - so not without some external expertise.

Not necessarily because a religious story should be taken as evidence, but because people over the years have attempted to prove or disprove the book by proving or disproving whether this type of voyage was possible, and whether a person with no blacksmithing experience could have formed the tools needed, and worked the lumber as required. Here's one page with a little information: bmaf.org/articles/another_idea_nephis_ship__carr

Kon-Tiki had a crew of six. Do you have any evidence that the construction techniques can scale up to something that can transport 30+ people?

@Mark To bring more people you don't need a bigger raft, you can have a fleet of rafts. The longest raft voyage, the Las Balsas, used a fleet of 3 rafts to bring 12 people. Scale up as required.

@AdamDavis The idea that Lehi's party had no blacksmithing experience is debatable. I can't find the references now, but I've seen articles presenting the idea that, based on the language and ideas he used in his writing, Nephi was most likely a smith by profession before his family's exodus.

@MasonWheeler That is certainly possible.

There is nothing inherent in Kon-Tiki that requires blacksmithing. They did know about currents and where they would take them, but the OPs group don't care where they are going. For navigational knowledge you substitute luck. Much more unlikely things have happened in novels.

Kon-Tiki's expedition actually benefited from a lack of blacksmiths. Engineers suggested wrapping the logs with chains, rather than ropes, to prevent the ropes being crushed by the logs. As it turned out, the logs formed indentations; chains would probably have sawed through the logs and damaged the raft. Lower tech actually made the voyage safer, at least in that instance.

The choice of a northerly route (as in the question) would make the use of a raft much less successful. The seas would be rougher and the climate colder. This would mean that, to avoid deaths due to exposure, there would need to be some form of enclosed cabin where the people could shelter from the wind and water. Putting a weather-proof structure onto a basic raft would make it top-heavy and unstable, and also make sailing and navigating the raft more difficult.

@SteveBird some lightweight structures, like tents, would provide the needed protection without changing the center of gravity significantly.

I think that it's unlikely they would be able to manufacture a tent that was sufficiently sealed that it would keep out water from waves sweeping across the deck. The tent would also act as a subsidiary sail, especially in high winds, complicating handling and navigation.

@SteveBird No structure they build would be water tight, and it wouldn't need to be. They won't be under constant storm conditions. A low tent (you don't need to be able to stand up in it) on a large raft would act as a small sail, but it doesn't necessarily mean it would prevent them from handling. The OP has already said that they don't know they are heading for California - so what navigation? As far as I can tell the story simply wants them to exist on the water for a period of time. It certainly won't be a picnic - it only has to be slightly better chances than certain death.

"so what navigation?" - if they're not navigating, how do they know they're not sailing around in big circles? Even if they don't have a fixed destination, they want to know they're not going to wash up on the shore they left a few months earlier. Also I never said anything about the storm conditions needing to be constant. A day-long storm repeatedly drenching them with cold water in combination with a frigid wind will probably do the trick.

@SteveBird The question is, "What will they need in terms of construction supplies and construction facilities in order to build a ship strong enough to get them across the pacific? How likely is this little band to pull of this kind of a project?" and then supplementary info is given regarding what will happen to them, but nothing suggests that they have or need navigational prowess - they are going into an ocean current that will do the work for them. Consider commenting - or asking a new question - if you need additional navigational ideas.

@SteveBird You might as well state that anything less than a large metal cruise ship will be "much less successful". I don't disagree. Given the level of sophistication, though, the question asks if it's possible and I'm proposing a solution that has very, very high risk - but may fulfill the need: "Escaping by getting out to sea is of the utmost importance." If you have a better, more likely to be accomplished by this group, proposal then please add an answer. Yes, this solution may still fail - but of all those presented so far it's the one with the most evidence of possible success.