The phrase "already realizing that" is correct and usable in written English.
It can be used when indicating that someone has come to an understanding or awareness of something prior to a certain point in time.
Example: "She was already realizing that the project would require more time than initially anticipated."
Alternatives: "beginning to understand that" or "starting to grasp that".
Marketers are already realizing that businesses that are able to humanize their brand are the ones who are standing out; and I believe this will only increase in importance in 2015.
We are already realizing that the subjects we studied in college might not be very useful in the business world and are adapting our ideas and skills to the changing economy.
Companies are already realizing that "virtual advertising space can be displayed a lot side "in-game" experiences with the captive user audience.
Republican House members (some of them, at any rate) are already realizing that this may blow up in their faces with the voters, and the Republican senators really really wanted to avoid actually going on the record.
Or, if you or your fiancé has a large family, you could say, "We already realize that, once we invite our families, we won't be able to invite many of our friends and coworkers".
The proud patriot of American ideals already realizes that democracy cannot be installed in other nations until our own experiment is perfected.
In my opinion, Twitter is pointless, and many people will — if they haven't already — realize that.
Though it means you will miss the reception, you already realize that you can attend the ceremony and be home by sundown.
They already realized that the thing to do was to get people vocal, almost an interactive type thing, so that the audience feels superior to the film.
Or, a patient may already realize that his or her insurance policy, or the lack thereof, won't cover certain medical expenses.
From those records, it is clear that King John had already realized that he would have to grant free election to ecclesiastical offices and meet the barons' general demands.
