Etiquette suggests parents of the groom write a letter to the parents of the bride. We haven't met yet. What things are appropriate to write?

I have never heard of this 'etiquette'. Everyone usually meets at the engagement party. I see why you are asking. It would be difficult not knowing them or their customs, or how they relate to their son, but I think inviting them over for dinner would be the best thing to do. You would want to meet them face to face before the wedding.

Tick

I think you should meet in person which is your children's responsibility to arrange. Dinner for both sets of parents would be fitting, and if any of these parents are divorced, a few dinners might be needed.

I've heard of the grooms parents writing to the brides parents after the wedding if the brides parents have paid for the wedding or most of the wedding. This would be a heartfelt, handwritten thank you such as, "Every detail of Dave and Melissa's wedding was absolute perfection. We've never seen our son so happy, and are over the moon to have such a lovely daughter in law. Thank you for all that you did to provide the kids such a memorable and lovely day."

I have no idea what you'd say in a pre-wedding letter to people you've not met but perhaps, "We are so delighted with the news of the marriage, and so thrilled with our son's fantastic choice of a future wife. We very much look forward to meeting you and hope you can join us and the kids at our home for dinner on Saturday (date, time) so we can have a chance to get to know one another". I never heard of this as a tradition though.