Remember, that if your scenario has a traversable multiverse at all, it's unlikely that just the one constituent universe has created a multiverse traversal capability.
If you have any version of multiverse with countably-infinite variations upon the theme, it would probably have a ('lesser', but still) countably-infinite number of traversers arriving at a countably-infinite number of other worlds (some 'virgin' and new to the possibility, some already having had their own departure-tech and possibly even would be more skilled (and/or reckless) with the ability, and/or dealing with those that intrude with their own).
One way or another, Evil Twin/Good Twin will probably happen (and probably... because why not... Much Eviller Twin/Insufferably Good Twin/etc, or maybe just a lot of Blue And Orange Morality where you can't even tell who is protagonist or antagonist on the grand scale).
Unless you have something (e.g. Baxter/Pratchett "The Long Earth" setup) that makes 'prime Universe' somehow more unique[1], which does rather depend upon one or other '-centric' viewpoint (even in TLE, though, we discover that 'step East/West' isn't the only way to go, nor is Earth necessarily the focal factor for any given 'line' of universes).
(I suppose there "has to be a first", just like we may just happen to be the first (and/or last) inhabitants of our own universe (or at least easily testable parts thereof[2]), but it's highly unlikely that we're actually that special, if it turns out to actually be easily doable. And if it's not actually so easily doable, then that might be the reason why we don't have good evidence of anyone doing it before. - But still more likely that they have, just not left any/enough-of-a mark on our own history, than we're going to be the ones who kick it all off.)
Choose your own scenario. For every Sliders treatment, a Star Trek or Red Dwarf or Primeval-type treatment. And countless literary variations that... I very nearly went and tried to explain[3].
[1] In 'The Long Earth', it seems less a factor of the universe, more a factor of what happens when you force a degenerated 'Longness-unable' arm of the general homid races to sit in one place, crowd together and have to become 'civilised', as opposed to just passively exploiting the apparently easy ability to step 'sideways' and maintain a more pre-agricultural hunter-gatherer lifestyle as befits all such nomads-across-worlds. Thus, in this 'Earth prime', the special thing seems to have been not being dimension-capable.
[2] What with Relativity, it's also possible that every suitably intelligent and enquiring civilisation that develops has developed 'before' absolutely every other possibly detectable civilisation has arisen. That is, of course, a problem/side-effect of regular space-time. And who is to say what meta-relativistic effects might occur when it comes to trying to work with the meta-chronology in a possibly hotch-potch multiversal configuration. 'Narnia time' could be at play, or 'rumpled paper touches rumpled paper' (you can jump across, where it touches another universe, but then you have to wait until the corrugations in the 'time dimension' coincide again, for that or any other spacial meeting-spot), or 'skewed pack of playing cards' (each card 'contains' a roughly equal history, but jumping from one to another sends you futher up/down its timeline), or there's temporal circularity wherever all dimensions (including the non-space one(s)) wrap around.
[3] There's the short story (a "Tales From The Spaceport Bar"-type one, can't remember who wrote it, but probably one of the '50s/'60s/'70s types) with the guy with the Universe-Hopping-Backpack. Used it to jump universes a few times, may now be looking for 'home' again. Gets chatting to a 'local' guy (in the latest univere he's passing through), probably in the aformentioned bar, who turns out to be a bit knowledgable about the theories involved. Local guy points out that the energy needed to step from one universe to another would be... well, about as much as contained in any given universe... Are you sure you've arrived from another universe? "Pish tush, the backpack works, just watch me disappear onward to the next universe (as I try to find home again?)..." Backpack-Guy 'jumps', backpack does indeed need as much energy as is in a universe, i.e. the universe he's departing, meaning that there's nobody now there able to marvel at how Backpack-Guy just vanished, because they had vanished (and the bar, and the whole universe). And, of course, that has more than a few implications for BG's quest to 'find the way back home, from where he started jumping'. ((Though not all such treatments that I could convey are actually built upon such deliberately exact principles. Most are, at best, written in exactly as much as they need to be as a secondary plot-excuse to support the "everyday modern man from our type of world finds himself somehow in a parallel and Vikingesque alternate present, due to many-worlds theory and some historic chance change in how history went" conceipt which is the true aim of the tale.))