If I want to refer to the time about two minuites before now, which one should I use?
- I just know that...
- I just knew that...
or either one? Click to view the N-gram
If the intention is to convey that I now know something that I didn't know until about two minutes ago, neither of OP's suggestions are appropriate.
1: I can't say exactly what's wrong with Jack - I just know that I don't like him.
2: Jill says Jack is a convicted child molester - I just knew there was something wrong with him.
3: I just found out (or discovered, became aware, etc.) that Jack is a paedophile
In #1 and #2, just is really an "emphasising modifier" for know (akin to only, simply, merely,, etc.).
In #3, just is a "temporal qualifier", effectively meaning very recently, not long ago.
In this particular context there's nothing to be gained by comparing NGrams for present and past tense, they simply reflect the fact that the usage illustrated in #1 and #2 above can occur in respect of things believed/known both currently and previously.