Science is intrinsically a bottom-up process. We build models that fit a data set, then try to integrate those models with other models that we fit to other data sets. That models could then contradict each other -- is actually expected of such a bottoms up process.
Most of the contradictions and conflicts within science, however, are WITHIN a particular science, as the sub-fields within a science tend to interact more than there is interaction between sciences. A good example is the age of the universe, which for many decades was estimated as ~13.7 billion years per Hubble expansion, but our stellar age models said the oldest stars were about 15 billion years old... The conflict was finally resolved after many decades by the Big Bang model changing its assumptions of a zero and unchanging cosmological constant.
A conflict between sciences was when paleontologists and geologists said that South America and Africa were once connected, but planetary physicists said this was impossible. This also took decades to resolve, when the planetary physicists eventually realized that magma was "fluid-like" and could sustain currents and continental floating.
So the presumption of a single "truth" is generally assumed, but the science of a particular day will often include a LOT of contradictions about what the details of that truth are -- and the competing models are both used for scientific work in their particular fields despite their not agreeing holistically. Science, therefore, so long as it is an active field of study, will be intrinsically logically incoherent.
There are various responses to that incoherence. One, the "top down" approach you asked about in comments, is to try to force coherence on science, to fit a global model. The last attempt to do that within the science community was with Logical Positivism, and LP failed to come up with a workable methodology for science. Several ideological movements have attempted to do this. Soviet Science for instance tried to make all science coherent with party ideology -- which led to abandoning falsification testing for the resulting theories. Creationism Science tries to do this, and then makes use of Quine-Duhem's principle that one can ALWAYS come up with another theory that fits the facts, if one is willing to go very complex and speculative. Creation Science relies upon things like varying light speeds, God pre-setting the universe to look like it had a history, etc. and also abandons falsification testing.
Another response is to try to unify the sciences through reductionism, and treat the failures so far as just potholes along the way, to eventually be overcome. Taht was the dominant paradigm in science for the 20th century. However, as the SEP article on scientific reductionism notes, we have a theory of reductionism, and it appears that our sciences do not satisfy it: https://plato.stanford.edu/entries/scientific-reduction/ There is just too much variance between the subjects studied at higher level sciences, and the building blocks they reduce to. If science is to be unified, we would need as a minimum a theory of emergence as well, and we don't have anything like such a theory today.
Sciences today operate on scientific pluralism -- there are multiple sciences, their models do not cohere, and one can and does get contradictions in predictions between them. Each such contradiction becomes another opportunity to add further "problems" to one or another science's evidence set they need to account for in future theorizing. But full reconciliation will remain an aspiration, never an accomplishment.
As some comments to the question note, the presumption of a single truth IS just a presumption. It is a mostly very useful one, but the peculiarities of both quantum mechanics and general relativity have pushed the envelope of what one can call "truth".
