Maxperson
Morkus from Orkus
Let us take the Big Bang as an example.
Back in 1902, Einstein's version of the Universe in General Relativity was static - neither growing nor shrinking in time, and having always existed and always would exist. In 1922 and 1923, Edwin Hubble showed that the Milky Way was not the whole of the Universe, that there were other galaxies outside our own.
In 1927 Georges Henri Joseph Édouard Lemaître put forth a model of an expanding universe, based on Einstein's equations. Einstein admitted the math was good, but had issues with the non-static result. In 1929, observations by Edwin Hubble (because of how things got names, a lot of people don't realize the initial theory was Lemaître's, not Hubble's) backed up Lemaître's theory. For many years, there was a great deal of arguing over this - many, including Einstein, were not comfortable with the idea of an expanding Universe, thought Einstein actually encouraged Lemaître to keep working on the theory. In 1948, Ralph Alpher, and Robert Herman worked out that if the Universe had once been a small, dense, hot ball, there would be some leftover background radiation to the Universe. The existence of this radiation was discovered in 1964 by Arno Penzias and Robert Woodrow Wilson at the Crawford Hill location of Bell Telephone Laboratories in Holmdel Township, New Jersey (scooping several other groups in so doing).
Since then, the model has been updated several times over.
This is pretty much the poster child for science overall *not* making assumptions. Each step of the development of the model has been accompanied by wrangling, lots of math, and experimental verification, rather than flat assumption of correctness. Yes, today is it taken as likely the best guess we have as to how the Universe came to be - though it is understood there's still stuff about it we don't know. But, there are still a couple of competing theories out there - they either make predictions that don't match observations nearly as well as Big Bang does, or are actually non-falsifiable (either practically of the moment, or outright theoretically).
I get that it wasn't a flat assumption. I'm not saying that. However, assumption is there. It was assumed by Einstein that due to his math, the universe was constant and not moving. It was then assumed by the others due to their math that it was moving. It was then assumed by Herman that there would be radiation if the universe began as a small mass. The next assumption is bolded above. The existence of radiation was discovered. Whether it was "this" radiation or some other radiation isn't known, but is assumed to be from the big bang.
I'm not disputing that the assumptions of science aren't grounded in math and other more solid approaches to the blind faith of religion, or that those assumptions are not subject to challenge and change. That's a stark difference from religious assumptions. However, they are still assumptions.