The Buddha found certainty by only trusting what could be directly observed and verified (is the 'falsified' a pleonasm?). The characteristic of impermanence (anicca), for directly observed things (not inferred 'things' like Plato's Forms or God), is present for all that has been seen at all scales, whether a proton a sandwich or a black hole, whether at the time of the Buddha or now. One can posit permanence somewhere beyond what is observable (the Hubble volume these days), but it would be a hypothesis outside of all observation up to now.
That impermanent experience, is unsatisfactory (dukkha) is simply logical, as even happy experience ends.. (this is subject to the economic problem, 'unlimited wants, limited resources', but then space-time is not a resource we can extend anyways)
Direct observation of non-self (anatta) with regards to 'oneself', is inferred until nibbana.
The modern world offers more well defined insights along the lines of the Buddha from the scientific method imo, as the two share a core requirement for observational verification. You have Copernican, Gallilean, special, general relativity and relational QM, which explain conditioned experience progressively more and more accurately. Science is heading towards having to accept anatta soon because what is directly observed now is no different from what was observed 2500 years ago - impermanent and empty of self referential information.. or likely more 'impermanent and describes observed experience less accurately if observer independent or self referential properties are assumed'!
Both the scientific method and the Buddha however, cannot offer 'certainty' for conditioned phenomena. QM states that the Sun will not come up tomorrow with some probability (say quantum tunnel into a black hole), statistics cannot reject the null hypothesis at the 100% significance level. It is not necessary to be skeptical about impermanence with regards to conditioned phenomena however, because there is not a single bit of observable and verifiable counter-evidence up till now.