"having realized" is correct and usable in written English.
You can use it to indicate that someone has come to an understanding or awareness of something. For example, "Having realized their mistake, the team quickly moved to correct it."
Congress was tone-deaf, perhaps not having realized the electorate has changed.
Weinberg died in 1996, having realized in his final days that he would never hear the opera.
He gazed at the woman who inspired him to dream, having realized, he said, "the dream was her".
The team returned having realized not only their own dreams but those of many of their neighbors.
Just before the doors closed, one brother jumped back in, having realized he'd gotten off on the wrong floor.
Who'd have thought in 1966 that we'd one day be riding through southern England, none of us having realized the futures we predicted for ourselves.
Humanitarian groups started lobbying after the 1991 Persian Gulf war to curb the trade in conventional weapons, having realized that Iraq had more weapons than France, diplomats said.
There is an undoubted comedy in Orwell's never having realized that what was obviously utopia to him might strike at least half the population as a chaste nightmare.
The men had hidden in the closet, having realized, apparently, that the authorities were on the premises, Chief Deputy Long said.
Carlyle, for example, recently closed a $2.3 billion fund, having realized a five-times paper profit on its investment in insurer China Pacific.
They became excited about discovering ever more advanced concepts, having realized each new fact was another weapon in their intellectual arsenal.
