Short-answer: we don't and can't, since you'd need to use the vaccine for a long time.
Better answer: the vaccines are new but the individual systems used to develop them are not, and we have historical trials of a lot of the same techniques which show no long term risks. The biggest unknown has always been the risk of triggering a short-term, unexpected primary immune response that causes harm to the recipient. In the vaccines being developed, that has generally not been found to be the case, and since they're based on the virus currently infecting people we would not expect a response worse then that (which is to say: the components of vaccine use are all well studied, these are understood and safe materials).
The other issue is when we talk about "rushing" vaccine research, this does not involve shirking safety research - i.e. consider the influenza vaccine which year over year is basically a new vaccine we develop quite quickly. What it does mean is that you overlap the stages of vaccine development: normally if you have a P3-trial vaccine, you'd wait till that trial was successful before building the factory to make it. Instead, companies are being paid (or paying themselves) to build facilities and scale up production as soon as they get to the P3 trial stage - financially it's a huge risk, since what they have might not work, or might have an unacceptable risk profile in those trials - which means all the investment is a dead-loss.
This is where government steps in (and has stepped in in places): by guaranteeing the investment on getting those facilities out, it means if your vaccine works then you're ready to go and it's in production right away - as opposed to being another year to 2 years down the line while you work on manufacturing.