Sorry, I mixed your comment with somebody else's which used the word "emerged" and argued delta and lambda appeared because of the unvaccinated.
On the rest, not arguing on the mechanics and dynamics of the epidemic.
The only meaningful effort made to systematically track the vaccination effort effects since day one is Israel's 580K control group matched cohort. The UK is not quite at this level of details, let's say. Those two countries are not enough.
Most of the rest which I seen is "let's throw a model at the wall and see what sticks", followed "the study is under-powered but let's publish anyway", concluding with "have clueless random msm journalists and anti-covid-vaxx sleuths misquote the results".
On that account, I don't really trust anybody's observations either way quite yet. We'll have to see the post-mortem in a couple year's time.
If you read GP's comment closely, it's worded such that it acknowledges this point (though I admit it could be made even more clear).
Now consider the massive increase in dominance of these strains, not where or how they originated. That is what's relevant to the sources I've provided.
Hopefully with that cleared up, through your "temporal logic" and "direct inductive reasoning" you'll see that the timeline on which these variants came to dominate matches very closely with the mass vaccination efforts.