'survive' is an interesting question. The 'black death' in the 14th Century wiped out approx. 20 million people in Europe, which at the time represented one third of the population of Europe. So if you are comfortable with one in three people dying then no, we don't need vaccines. Was the polio vaccine not essential, in the 50s?

You can also ask, how did we survive without electricity, air travel, steel ...