The phrase "without me knowing" is correct and usable in written English. It can often be used when referring to something being done without the knowledge of a particular person. For example, "My friend secretly enrolled me in a yoga class, without me knowing.".
You know, in some ways, without me knowing it consciously — because I did the first draft of "Two Lovers" on my own — "Two Lovers" is sort of about him.
"The person I just met will be able to enter my head and know what I am thinking, possibly without me knowing.
"Put his hand in the cookie jar without me knowing.
"I'd hate it if people on the street recognize me, without me knowing".
Nearly every day, I am reminded just how much certain people in this country hate me without knowing me--by a breaking news alert or a campaign sign or a confederate flag or a fanatic overheard on the street or a fresh piece of hate mail in my inbox from either a third-grader posing as an adult or an adult with a third-grade literacy level.
"You had your reasons to despise me without knowing me, but I dared not challenge them.
And so without me really knowing it, that window changed my life".
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com