Are there any general introduction sentences for A Christmas Carol that I can use easily for an essay response?
It depends a lot on the essay question that you are responding to, as the first sentence of any essay response should really try to rewrite the essay question to show to the marker that you have clearly understood the question and know what is required of you. However, it is also possible to begin an essay question with a much more generic statement about the text under discussion, where you recognise its popularity or literary merit. For example, you could begin any essay on this text with the following sentence:
Since its publication in 1843, A Christmas Carol is a text that has captured the essence of Christmas like no other, with many people choosing to read and re-read it every year during the festive period.
You could then use this as something of a springboard to help you tackle the specific question that you are looking at. Such an opening would also engage the reader and show your greater contextual knowledge of the text. Another example that you could use would be something like:
Scrooge is a character who has entered the English language and is associated with stinginess and greed thanks to A Christmas Carol, which is a text that has taken on a life of its own and reached a level of fame that would have astonished Dickens were he alive today.
Any generic opening sentence like this about the novel as a whole would be suitable to begin an essay, as it provides a general introductory sentence to set the context of the question.