It's inevitable because even though one variant may become dominant, there will still be isolated pockets of the other variants. It's very unlikely that these variants will be entirely eliminated across the whole globe. Look at the epidemiology of HIV and the spatial distribution of variants as a point of comparison. Likewise for other viruses. Even if these other variants continue to evolve from the initial root, they will still be phylogenetically distinct from the current omicron clustering, somewhere intermediate between the root and existing omicron cluster. If it's out there in the wild, it will be picked up by PCR eventually. If it's not out in the wild, that big gap will remain, and a lab somewhere has questions to answer...
The starting point for the omicron cluster would be an interesting bit of information, but it doesn't necessarily have any bearing on where the intermediate strains are located. But none of that matters. If it's out there, it will eventually be picked up by PCR. We can use phylogenetic analysis to retrospectively reconstruct the evolutionary tree of every organism we have sequenced to date. Doing it just for the coronavirus variants is not hard (I have done it in the past including bootstrapping). Whether it's a month, a year or a decade from now, we will be able to answer the question by reconstructing the tree.
This is really basic bioinformatic analysis, in routine use for over two decades. None of this stuff is remotely new or groundbreaking.
The other questions you are asking are not really relevant to the problem. The virus does not survive long outside a host; it has no bearing upon the problem at all. The same applies to inside the host. All variants will continue to infect and propagate themselves to varying degrees within the host populations. It's endemic at this point.
One other point to bear in mind is that the mutation rate of the polymerase is effectively a constant, in terms of mutations per n kilobases. So we would expect all variants to accumulate a certain number of mutations averaged over time--the sequence will not remain static since the virus has to continually be passaged through mammalian epithelial cells to maintain and propagate itself. There will be some variation, but if it's been frozen down and manually propagated, it may have a dramatically different number of mutations compared with the other contemporary strains that have spent most of their time in living hosts.