I managed to get a paddle in the version before it was implemented that you could make boardsd with a stone axe:
On the island in the summer there are nettles growing. Harvest all of them, and plant their seeds, and process the fibers for yarn and then cord and then rope. Try to get perfect or fine yarn and mix only those into cords. If you can get a fine nettle rope, you will be able to make a fine stone axe, and with a fine stone axe, you can make boards. There won't be enough nettles in the first year for this, but by the second year, there will be, if you plant a lot of them in spring.
Also practice swimming near the shore -- if you can train up to 100 swimming then you might be able to get to land faster than the nettles plan. Figure out how many tiles you can swim by swimming along the shore of your island, it will vary depending on endurance, then zoom out and consider your options. Always stop swimming before your fatigue is equal to your swimming skill, and stay just one step away from safety while training it.
It may also happen that when winter comes, the sea ice will freeze and you'll be able to get to a bigger island, or even the mainland.