That's very silly of this game

[Homocommando]

So apparently I spawned on an unpopulated island, with my father killed by a glutton, yet we brought no punts, paddles or axes to this island, we just magically appeared here, and now my character is completely unable to fashion any kind of tool to help him get out from that island

[JP_Finn]

With current version, you should be able to craft boards even with a stone axe. Will take some time, but at least you can fashion a paddle.

As for appearing on the island, maybe your character and dead ol’ dad saw the glutton from the water, got excited, chased the glutton. And in that excitement forgot to pull the punt to shore. Get in trouble and come back to the punt and paddles missing.

[Homocommando]

With current version, you should be able to craft boards even with a stone axe. Will take some time, but at least you can fashion a paddle.

I was playing on 3.62, didn't bother to update. ...And with current version you mean 3.8x, not 3.71? ...

[JP_Finn]

Yes indeed, v3.84.

[Plotinus]

I've gotten off the island in 3.62, that used to be one of my favourite starts.

Harvest all the nettles that you can and plant a giant field with all the seeds, and then next year harvest all those nettles too. Make nettle yarns until you have enough fine/perfect ones, then make nettle cords until you have enough fine/perfect ones, then finally make a fine or perfect nettle rope. With that, you can make a fine stone axe, which can make boards.

Also, in the summers, practice your swimming until you get the skill to 100%, you might be able to explore some nearby islands that way and get even more nettles, maybe enough to not have to spend a couple years on the nettle rope project, you might even be able to get to a village that way, and can work on reputation building and maybe get an axe.

Put bear traps along the shore for catching seals to make warm clothes. Prepare a ton of wooden blocks to survive the winter, you'll need the fire going almost continuously.

In the winters, when the ice is stable, you may be able to walk across it to more settlements or to a bigger island where there will be more game spawning.

[Homocommando]

Harvest all the nettles that you can and plant a giant field with all the seeds, and then next year harvest all those nettles too. Make nettle yarns until you have enough fine/perfect ones, then make nettle cords until you have enough fine/perfect ones, then finally make a fine or perfect nettle rope. With that, you can make a fine stone axe, which can make boards.

With that much time I would probably be able to just wait until I don't freeze to death in water and swim to the mainland.

Also, in the summers, practice your swimming until you get the skill to 100%

And what am I supposed to do in winters? With nothing else to do I may as well just go swimming in cold water and warm up by a fire to prepare my swimming skills, so I can escape immediately when it's warm enough.

Put bear traps along the shore for catching seals to make warm clothes. Prepare a ton of wooden blocks to survive the winter, you'll need the fire going almost continuously.

Wiki says seals are not attracted to bait, and I haven't seen one yet, so I am not sure that would be worth it?

[Plotinus]

They're not attracted to bait, but they like to come on shore, it's worth a try, I usually catch a few. In winter it gets very cold. You're going to be sitting by a fire almost continuously. but while you do that you can make more firewoods for your nettle plantation (3 branches or 3 firewoods per tile you want to plant on).

Hypothermia sets in very fast when the water is cold, you won't be able to stay in the water long enough to get even one skill up in Swidden, but do start swimming as soon as you can. If you're close enough to the mainland then you'll probably be able to get there in one summer. It depends on your endurance. If you have high endurance then you may be able to swim 7, 10, 14, tiles. If your endurance is very low, then you might not be able to swim one tile. You can check how far you can swim by counting until you get moderately tired, then turning back. there are 64 zoomed in tiles to a zoomed out tile.