If you want something that still tastes fresh and sweet, you can freeze your jars. Freezer jam usually uses pectin and sugar because that's how you get jam texture. Pureed strawberries are really runny. You should also anticipate losing some of the sweetness of the strawberries, unless you can flash freeze them somehow. But you would lose that if you went the fermentation route anyway.
As written, this is a pretty terrible idea, though. You still need to do the sanitation process on the jars, and the prospect of getting kill-you-microbe soup is high without involving a preservative of some kind or a yeast to nudge the fermentation the right way. Strawberries are high in water and moderate in sugar, which makes them really hospitable to bacteria and fungus. Mold, yuck.