I think the important parts have been covered, but maybe I can reiterate somethings.
Firstly, my strong opinion with apologies but:
No!!! you should not wait longer, you should be conversing asap. If it scares the hell out of you now, all the more reason. Good language exchanging is so valuable.
But you need the right partner and a good mindset yourself, so there may be poor initial steps, but you’ll get there.
That the learner is a super beginner doesn’t have to be hell.
I’m sorry again for the strong opinion but I really disagree - the challenge is to keep face (not that hard with some practice) and the awkwardness is only if you take it too seriously and lose face.
Structure to your meeting is really important, and best to agree on in advance.
I can really recommend meeting for a set time (say 2 hours), splitting that in half and strictly conversing in the target language only.
2nd structure point is conversation time followed by language advice/correction time. The proficient speaker should listen and seive out the bigger language difficulties that repeat during the conversation. Flow is so important, and corrections shouldn’t be made until a safe “correction time” later. It’s a tough job for the proficient speaker because they have to multitask: leading the conversation in most cases, keeping face and supporting the learner whilst still making it realistically challenging, even incorporating elements of SRS into the conversation, and then tracking the learners overall “performance” to isolate the more important points to feedback on with advice/correction later. Like anything, if you do a good job for them, hopefully they’ll return the favour.
Topic wise, you’ll need something, but on the other hand learning benefits from a sense of spontenIety. And in that, keeping face is one important thing, but keeping it fun is even more important. This is one point on why the particular partner is important, because a shared sense of fun works best, but like any partner sometimes you can’t click, it’s nobody’s fault necessarily, you move on with the conversation or move on with a new partner.
Probably I wrote way too much, but I hope you have a good exchange.