I wouldn’t ask someone their pronouns as a conversation opener because it makes some folks uncomfortable. For example a trans person might wonder something like “Do they ask that of everybody? Do I not pass?” if “passing” is something they care about.
It’s better to just correct mistakes when you make them. It’s also just something you’ll pick up automatically talking with people they know, and like here where the hypothetical person’s pronouns are ambiguous you can fall back to they. And when taking to the person themselves you are going to be using you anyway.