How to create a publicly visible, provably random seed ahead of time?

Imagine that you are hosting a debate with n participants and you wish to split them in half in a completely random fashion.

One might do so by creating a list of participants, randomly shuffling that list, then forcing the first n/2 participants to debate as a team.

If this debate was particularly important, however, we would want to ensure that the teams we have created are provably random in a way that is publicly visible. We want to be able to show that the teams we have created are not the direct result of any human's decisions. Would there be a way to do this?

I believe this problem boils down to the issue of creating a seed for a random number generator that is based on the state of the world at a particular time, but I'm not sure. Is this a problem software engineers have tackled before, and is there an API out there for this?