I wrote up a long discussion of Einstein's fame here — the TLDR is, yes, he was extremely famous in his time, though not exactly in the same way he is today. Even before the atomic bomb (and his supposed association with it), he was popular enough to be on TIME magazine twice, and after the atomic bomb he was seen as a modern-day prophet.

The Einstein we talk about today is almost totally devoid of politics, almost saintly/grandfathery. The Einstein of his own life took strong political positions that were not always in line with the consensus thought of the day, and earned him an FBI file hundreds of pages long.