Efficacy has been proven to a high enough degree of certainty that these vaccines are now being submitted for approval. Safety was largely proven in Phase 1/2 trials (before tens of thousands of people were injected with the stuff for Phase 3 trials). And all signs continue to show the vaccine to be safe (and data will continue to be collected for at least a year or two for the various Phase 3 trials).

Maybe "you" need more data for whatever concept you have in your head of how this should work. However, within the scientific community involved with developing and approving these vaccines, the data we have is sufficient (pending review of course).

If the data we have is sufficient, then why hasn't it been approved yet?

The data was literally just released.

Moderna and Pfizer submitted for approval shortly after they released their initial Phase 3 results. Approval is expected to be expedited, but will not be instant (I've read a few weeks, assuming no problems). Oxford/AstraZeneca will likely follow the same course now that their results are available (they were waiting for enough people in their trials to become infected, same as the other Phase 3 trials).

It is widely expected that large scale distribution of these vaccines will begin in late December.

Wait, so was the data just released or has the scientific community had enough time to analyze these results and determine that the vaccine is safe?

Is this some attempt at a "gotcha"? It's all over the news, I'm sure you can Google it. CDC Director just said first vaccines should got out second week of December.