Hash functions reversal

How do we know that hash functions cannot be reversed? An example is often given of two primes and their product, but any composite number that is the product of two primes has, by definition, exactly 2 natural factors. In the case of hash functions, things are different.

Have there been attempts to reverse hash functions, and if so, how many have been successful? Are there any theoretical works on this topic? Is there, for example, some justification for the unpredictability of hashes, like some kind of "entropy" (for example, the Caesar cipher has a very low entropy, and SHA256 has a high one)?

There have been a number of results showing that various hash function are not subexhaustively preimage resistant. The most prominent examples being Yasaki and Aoki's $2^{123.4}$ attack on MD5 inversion, Thomsen (building on work by Muller) $2^{73}$ attack on MD2 inversion, Leurent's $2^{102}$ attack on MD4 inversion. There are also other examples on some rarer hash functions.

There have been many attemps, but the safety mostly comes from the chaotic nature. Hashes compute a not-very-secure state, then add a couple bits and do it again. But because the states interact with other states, mixing and mashing, it is impossible to predict. It is pretty much like an accelerated double pendulum, no one can find a surefire way to predict pendulums (without calculus) let alone double pendulums. Similarly, no one can find a way to reverse engineer a hash (without A LOT, and I mean A LOT of computing power). https://www.clausewitz.com/mobile/chaosdemos.htm#DblPend