Moshe Rabbeinu could not have jumped in. He was commanded to raise his staff over the sea and stand there so that the Bnei Yisrael would be able to pass through (as we see in Beshalach 14:15 - 16 and 21). We also see that after Bnai Yisrael passed through, then Moshe Rabbeinu was explicitly commanded in pasuk 26 to stretch out his hand again to cause the sea to return to its position.
The implication of this is that Moshe Rabbeinu had to stand above the sea until it had completed splitting and then go through with the rest of the tribe of Levi. In order to complete the splitting, members of the Bnai Yisrael had to realize what must be done and jump in.
An analogy could be made to the fact that every member of Bnai Yisrael had to make the free choice to be liberated and to put the blood of the ram on his doorpost.