The first sentence is incorrect.
Indeed, the "que" word, where it is placed, implies a subjonctif verb. As in the first sentence, you used the imparfait de l'indicatif, it is incorrect.
In your second sentence, you used the imparfait du subjoncif. This is grammatically correct.
Yet, if with indicatif mode, imparfait is used very often, it is almost never used with the sujonctif mode. You should rather use the passé time (of the subjonctif mode).
Using the passé, we get:
Il était plutôt possible que je n'aie pas su (que) ...
But this way, your sentence is still awkward as
être plutôt possible means nothing (at least without the context).
I think you should get rid of the word
plutôt, as the use of "rather" is very English and usually it doesn't translate well in other languages.
plutôt totally messes up with the meaning of your sentence, maybe you should try to replace
Il était by
Cela était or by
C'était. You can also tell us a bit more about the context of the sentence for better advise.