After the splitting of the sea, the pasusk tells us in 14:31 "ויאמינו בה' ובמשה עבדו" - and they believed in Hashem and Moshe His servant.
It took them this long to come to the level of believing in Hashem? Only now do they see His strength because He split the sea - what about the various plagues they witnessed with all the relevant miracles? What about specifically the Plague of the First-Born where Hashem's tremendous strong hand was on display?
Why only now?
There is a difference between watching something and being a part of it.
Until now, with all teh plagues, all the signs, all the discussions, the Jews were on the sidelines. They were watching God take it out on the Egyptians. Sure they had faith in Hashem because of all they had witnessed.
By the splitting of the sea it was a whole new experience. They were part of it. They were being chased. They walked through the split sea. It was not just watching something happen to someone else. They were now a part of it. they experienced the "strong hand" first hand. Now they came to a whole new level of recognition and faith.
Being active, being part of an experience is different than just watching it happen from the side. That is what brought them to the level of emunah now that it says "And they believed in Hashem and Moshe His servant"