God, I wish teachers would stop asking this question. It's predictable, boring and shallow and I think it really shows more about teachers' desire to teach philosophy than wanting you to understand Orwell. Orwell acknowledged the point, but it's a tiny one in relation to the book.
In fact, you've given me an idea for a thread on this subject!
Now, for your question:
You're perfectly on track.
All Winston has is his memory of why he thinks the Party is lying. He personally remembers life
before the Party, but he has no external means of verification. It doesn't matter how many memories he has; without physical evidence, it becomes a philosophical question as to whether his memory can be believed. The Party is implanting false memories in everyone, can Winston be sure it isn't just his mind playing tricks? You can also take this back to "Insanity is being a minority of one." How does Winston know he isn't plain crackers?
The main single item which provides his physical link with the past is the snowing crystal ornament. He remembers one from his youth, but also, it's such an outlandish product that it could only have come from before Party rule. The object would be destroyed. It's a double-proof.
This then certifies that Winston's belief in his memory is correct and that there is an alternative to Party rule. He doesn't remember what that prior period had/didn't have, but he knows it existed and that the Party rule is not infinfite.
That then, shapes his philosophy.