To create a star all you need is gravity (and a bunch of gas and dust). A small fluctuation in the density of a dust cloud and you start accreting material until the local density becomes so high that fusion starts: pfff, star.
The Big Bang that started the Universe was a bit different – for a start gravity didn’t work! The Big Bang started with all of the matter in the Universe being at a single point – and the Universe is infinite, so that’s an infinite amount of matter at one point, which makes that point infinitely dense. We call that a “singularity” and at an infinitely dense singularity the normal laws of physics (including gravity) break. Fortunately, the Universe then started expanding…
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