When to approach my dissertation supervisor?
Guidance is typically provided on when you'd be expected to come up with your research question and your nomination of supervisor. Follow that guidance. If you haven't been told yet, then at least wait for the induction week to find out how things are organised. To kick off on choosing a dissertation topic and supervisor before induction really would be too early. Indeed, it would just look silly. So at the very minimum, do at least wait for two weeks.

On our (UK) Masters courses, the selection of thesis topic and supervisor doesn't happen until the second term. That's because the taught modules in the first term gives the students the grounding in research skills and research areas, and an introduction to the staff, that enables them to make better decisions.

If a student approaches a member of staff earlier than that, then a common response would be to note the interest, and to invite them to come back in the second term if they were still interested, but that there's no commitment to do so, as lots of things change after the first term.

An early approach does not necessarily make a good impression. It can look hasty. It can look like you're not expecting to learn anything in the first term.

And we don't really do reserving of research-questions, as such. At least, merely being the first to propose a research question for your dissertation doesn't give you priority in doing it. We work with students to get the best match of question, student skills, and supervisory support. If student B provides a better match than student A, then we'll recommend that student B does that dissertation, regardless of whether A or B proposed it first. In recent cases where we have had overlaps between particular students, then the research area has has sufficient open questions that the students have each been able to do a distinct dissertation within it (and indeed subsequently co-author papers together). So I don't really recognise this notion of "missing out on a topic".

It takes quite a bit of subject familiarity to understand where the open questions are, and that's one of the reasons why we wait until the second term before we get to topic and supervisor selection.