I certainly find the whole thing very hard to get my head around. As someone said earlier, it may be that we will always struggle to have an intuitive understanding of the very big or the very small in the same way as we grasp the actions of throwing a stone, for example.
However, there are multiple lines of evidence, some discussed earlier, which fit a model of an expanding universe that was much hotter and denser in the past (some 13.7 billion years ago). Primarily the bulk motion of the galaxies, the cosmic microwave background, and the ratio of elements observed all point in that direction.
Additionally, Einstein's General Theory of Relativity has great internal mathematical consistency, and has passed numerous experimental tests with flying colours. Leaving aside Einstein's attempt to fiddle things to make for a stationary universe (which he regretted) the theory itself actually predicts expansion...
Fully accepting that there are great unknown areas, such as the nature of the initial singularity (if there was one), inflation, dark matter, dark energy et al, it is hard to see there being a cosmological model which does not include a universe that is expanding, whether we hominids can grasp it entirely or not.
Nurse, where the fuck's my cardigan?
And my gin!