One way would be to consider the future of civilization. At the moment, we observe a Shifting Moral Zeitgeist. However, in the future we may see ideas about how to behave towards other agents settle down into an optimal region. If that turns out to be a global optimum - rather than a local one - i.e. much the same rules would be found by most surviving aliens - then that would represent a good foundation for the ideas of moral realism.

Even today, it should be pretty obvious that some moral systems are "better" than others ("better" in the sense of promoting the survival of those systems). That doesn't necessarily mean there's a "best" one - but it leaves that possibility open.