Was the knowledge gap because of something that you had failed to do, OP? E.g. a policy that you should have read but hadn't, or online training that you had been asked to complete but didn't? Or something that you should have known as a requirement for a professional qualification but had somehow missed or forgotten?
Or was it that your employer had failed to give you adequate training/induction?
If your supervisor had access to the same information as you but signed off the case regardless, then I think there definitely needs to be some accountability there. What's the point of having a sign-off process otherwise?
I presume that you didn't realise that you'd made a mistake at the time, and that you didn't attempt to cover it up? How did it eventually come to light? And what was the consequence for the client? Presumably your employer has some sort of insurance that would cover the employer for the impact of any poor advice that was given, but I guess that might be invalidated if the supervisor failed to do their job properly.
It sounds like a genuine mistake to me, and not something that I would consider firing someone for. Mistakes do happen, and this is even more likely if staff are new/inexperienced. Is your employer generally a fair and reasonable one? If so, I'd say that you'll probably be OK, but if not, all bets are off.
I think your best bet is to go in and be honest about what happened and why, highlight the fact that you got the work signed off by a supervisor as per protocol, apologise profusely for the error and show that you understand the consequences for the client and for the organisation, and explain how your learning since the incident means that this kind of error couldn't ever happen again. No point in beating yourself up about what went wrong, you're human and we are all fallible. Good luck!