It's possible. There's a subset of bacterial biofilms that are hydrogels. This is specifically what you want.
These aren't really jello, though, because that's a supersaturated solution of proteins. These biofilms are usually made of long chains of sugars, which are attracted to water.
Bacteria form biofilms to protect themselves from their environment. One of their other adaptations is entering a cyst stage.
Finally, bacteria are able to swap DNA.
It's possible that as the sea shrank, bacteria were left behind in pools. As these pools evaporated, the bacteria that were fittest to survive these changes were the ones able to develop hydrogels and the ones able to become cysts. After the pools dried out, the cysts could be carried by animals or other lifeforms to another pool, where the cysts would begin their life cycle again. At some point, the cyst-bacteria swapped DNA with the hydrogel bacteria. This created a new variety that could both extend its "active" period with hydrogels, allowing it to multiply many more times than the cyst-only bacteria, and able to survive the complete evaporation of the pools by forming cysts around themselves when the hydrogels eventually dried out. Eventually, the same way macro-lifeforms carried the cysts from pool pool, they eventually carried them to the sea. This allowed the bacteria to come out of their cysts and begin colonizing the sea with their hydrogel.