Hi, Joham.
I also feel the same way you do about this site. It's fantastic that we can get answers from so many knowledgeable people here. But some things we can do ourselves first and I think it's good to do them. There are some very useful tools available on the internet that can help you solve some problems you encounter. I'd like to show you what you could do before posting this thread.
First of all, there is Google. It's difficult to find certain things this way, but when you're looking for a particular phrase like yours, it's quite easy. Just search for
"greatly to my surprise"
with the quotation marks. The first result is your thread. This means something -- it's probably not the most common of all phrases. Of course, your thread wouldn't be there if you hadn't started it yet! Let's look at the other results. Most of them are texts written in very good literary English. This also means something. It means we are probably dealing with a correct phrase. There are 104.000 results. It's not very many, but enough to see that it's used. Perhaps its use is limited to literary English? That would explain everything.
Now, do you know about
this site? I think it may be one of the most useful tools for advanced learners of English. There are five English corpora there:
Corpus of Contemporary American English (COCA),
Corpus of Historical American English (COHA),
TIME Magazine Corpus of American English,
BYU-BNC: British National Corpus,
Google Book (American English) Corpus.
They're much more searchable than Google. If you try using it, you'll learn why. Anyway, here's what some of the corpora give us.
COCA: no results
COHA: 9 results (from between 1845 and 1924)
BNC: no results
With all this knowledge, you could make your question a little bit more specific. For example:
I know that the phrase "greatly to my surprise" is correct, but after searching the internet, I suspect its use is limited to literary English, perhaps older literary English. Am I correct?