I’d split it into few more specific functions so that each of them does less and has less variables, something like this:

def start_conversation(chat_id, user_id, %{gender: "female", user_id: participant_user_id}) do
  create_conversation(chat_id, participant_user_id, user_id)
end

def start_conversation(chat_id, user_id, %{gender: "male", user_id: participant_user_id}) do
  create_conversation(chat_id, user_id, participant_user_id)
end

defp create_conversation(chat_id, first_user_id, second_user_id) do  
  Db.Conversation.create(%{
      chat_id: chat_id,
      start_time: DateTime.utc_now,
      first_user_id: first_user_id,
      second_user_id: second_user_id
    })
end