Do you native speakers see these two as exactly the same?
That's her way of knowing the truth.
That's her way to know the truth.
However, it seems you're using "to know" with an inchoative aspect, which is not natural in English (find out, learn, realize, etc. are for the act of becoming aware).
Maybe it's BrE, but it doesn't sound so unnatural to me, and Bhai didn't mention it.