Sample size isn't the problem you think it is. The difference in statistical confidence between sample sizes of a hundred million (COVID vaccine doses) and a billion (flu vaccines) is basically zero.

Perhaps you could try to make a case that we need more time to evaluate the long-term effects of the vaccines. Historically speaking, we know that side effects for any vaccine are incredibly rare after more than a few months. mRNA vaccine technology has been researched for decades and there are no indicators that there are long-term complications resulting from their use. Other vaccine technologies show similar long-term safety.