You claim to be familar with the arguments and believe that proofs were offered. Hume's first line of reasoning was that the universe was more like an amimal than a watch. He reasoned that the universe could reproduce itself.
From Dialogues Concerning Natural Religion:
The world, says he, resembles the works of human contrivance; therefore its cause must also resemble that of the other. Here we may remark, that the operation of one very small part of nature, to wit man, upon another very small part, to wit that inanimate matter lying within his reach, is the rule by which Cleanthes judges of the origin of the whole; and he measures objects, so widely disproportioned, by the same individual standard. But to waive all objections drawn from this topic, I affirm, that there are other parts of the universe (besides the machines of human invention) which bear still a greater resemblance to the fabric of the world, and which, therefore, afford a better conjecture concerning the universal origin of this system. These parts are animals and vegetables. The world plainly resembles more an animal or a vegetable, than it does a watch or a knitting-loom. Its cause, therefore, it is more probable, resembles the cause of the former. The cause of the former is generation or vegetation. The cause, therefore, of the world, we may infer to be something similar or analogous to generation or vegetation
And he reasoned that the universe reproduced itself by:
In like manner as a tree sheds its seeds into the neighbouring fields, and produces other trees; so the great vegetable, the world, or this planetary system, produces within itself certain seeds, which, being scattered into the surrounding chaos, vegetate into new worlds. A comet, for instance, is the seed of a world; and after it has been fully ripened, by passing from sun to sun, and star to star, it is at last tossed into the unformed elements which every where surround this universe, and immediately sprouts up into a new system.
Does that describe any universe you know about? The man is speaking out of ignorance. The only proof there is that he didn't have a clue as to what goes on outside of earth's atmosphere.
Hume disergarded the watchmaker analogy because he didn't think that the universe looked like a watch. That is to say a precision instrument. He was blissfully unware of the laws of physics upon which even a small adjustment would result in an entirely different sort of universe.
His so called proofs were absolutely wrong.