What I want to say is that I write an analysis article about global population growth, and I worked on that with some public data. But I want to emphasis that I read a lot of data. Can I use "many" here?
This answer has to be a little complicated, because in the English-speaking world, there is a long-running controversy about whether data can be singular, and you should know about this controversy.
Some people say that data can only be plural; its singular is datum. Their reasoning is that data, like many technical terms in English, is borrowed from Latin, and the usual custom in English is to retain the Latin plural for technical terminology. By this reasoning, you should follow grammar like this:
One datum is insignificant. You can only get a statistically significant result if you collect many data.
However, over the last hundred years or so, many people have found it useful to treat data as a singular mass noun. The singular leads the reader to imagine data the way we think of other mass nouns: as something like sand or water, not as something that we count, like cars or houses. By about 1980, singular data became fully accepted in most formal writing. One reason for the change in grammar is that people seldom need to talk about a single datum, and datum became a rare word. Instead, when people need the singular, they follow grammar like this:
One data point, or one piece of data, is insignificant. You must collect much more data than that to get a statistically significant result.
As the word data became more common, people invented new meanings for datum, though only for use in very specialized, technical fields, like geodesy. When people need to make a plural for datum in these new senses of the word, it would be confusing to say data, so they say datums.
Today, the expectation that data is singular is reinforced by new phrases that exploit the singular number, like data type and data warehouse, where data is used as an attributive noun in a way that's customary only when the noun is singular. The common word database also leads people to expect that data is singular.
So, with one caveat, I recommend that you not say many data. Many data would require your reader to think of data as plural. For most English speakers today, using data as a plural is a little jarring—unless you are working in one of the rare fields where datum is still used as the singular of data. A helpful rule of thumb is: If you or your audience would say data point or one piece of data instead of datum, then you should treat data as singular.
These are good:
I analyzed a lot of data. [This is grammatical whether data is singular or plural.]
Much of the data suggests that global population growth is slowing, but a small part of the data raises doubts.
I wrote this article after examining a great deal of data.
In the last sentence, you could substitute a great amount of data, a large volume of data, or other common expressions that go with singular mass nouns. All of these phrases emphasize that you read a lot of data. Also, the verb examine makes that point more clearly than read. Usually we say that computers read data; human beings examine, consider, and analyze data. (Computers are also said to analyze data, but mechanically rather than thoughtfully.)
Some sources for data, such as public databases, are count nouns and should be plural:
I examined many public databases.
Here is the one caveat: Some people, a minority today, are sticklers for the older usage. Often these people work in positions of authority in organizations that uphold traditions, like schools and governments. In countries where English is not the native language, older forms are often taught, and correct modern usage is sometimes marked wrong on exams. So, know your audience. If your audience wants plural data, give them plural data. If you don't have specific information that your audience insists on the older grammar, then use singular data and avoid many.
"Many" doesn't work here because it's describing a singular noun. "Data" can't be "many" because it's just one thing.
If you said "I wrote this article after reading many books" it would be appropriate, because "books" is plural and when there are multiples of something, you can have many of them.
"I wrote this article after reading a lot of data" is a simple way of saying what you're intending to.
I wrote this article after reading many data
A datum is a unit of collected information. Here you are saying you have read many sets of collected information - in the sense of taking readings from an instrument, going through a process to sample and read the state of something, etc.
But I want to emphasis that I read a lot of data
Right here, you are expressing it in the way many would expect to hear it. I read a lot of data means you read a lot of articles or lists of data.
One problem is that reading data implies you are looking at lists of numbers, but doing nothing further. So even this:
I wrote this article after reading a lot of data
can come off as somewhat "incomplete" because you really should do more with data than just read it. This is probably better:
I wrote this article after analyzing a lot of data
As @BenKovits commented, data is originally a plural form of datum.
The word "data" is defined as a mass noun in Oxford Online Dictionary and it would be better to use "much" than "many" based on this definition. The linked Ngram Viewer, collected much data vs collected many data, seems to favor "much data" over "many data", but there is no much difference. It would not be incorrect to use "many data". It will depend on how you perceive the word.
As @PerryW commented, using "a large amount of data" or "a large volume of data" would be a good alternative.
Merriam-Webster confirms that the word data could be used as a singular or plural noun in construction. The word datum is not broaldy used in contemporary English.