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.

If removing 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.

The action of the subordinate clause is simultaneous to the one of the main clause: this means you must conjugate the verb savoir to l’imparfait du subjonctif.

From this rule, we conclude that the correct way to translate that into French is:

Il était possible que je ne susse pas