What is the ruling on chatting with male cousins for the purpose of getting acquainted, knowing that they are strangers and there was no prior acquaintance?

The default rule is that it is not permissible for a man to speak with a non-mahram (definition) woman except out of necessity or need, and from behind a screen, without softening the speech. Based on this, it is not permissible to chat with cousins via chat unless there is a valid need, while observing certain controls: that it be for maintaining kinship ties and acquaintance, that the image not appear via camera, and that the conversation be limited to acquaintance and news, with the acquaintance being between women if they are present.