First of all, modern Zionism began in the late 1800s/early 1900s, not 1948. But beyond that nitpicking, the answer is mostly no.

After the series of failed revolts against the Romans, desire among Jews for political independence by-and-large faded. There were, at various times, movements of Jews to migrate to Israel, but these were based on a (largely religious) desire to live in the Holy Land, not to obtain political control of it. The idea of nationalism didn't really exist yet, and political independence for Jews in the Holy Land tended to be linked to religious conceptions of the messianic era, not an actionable political idea.

At any rate, just because the Romans were gone didn't mean that things were ripe for re-asserting independence. Over the centuries many other powers controlled the area. While there were perhaps times of a relative power vacuum, they weren't the norm. More importantly, the actual Jewish population in the area was fairly small, so it would be difficult for Jews to actually assert their independence, when they were a minority.