The universe can't run solely on algorithms, except if you invoke "God did it! He created the first algorithm" or "The first algorithm just appered randomly out of nowhere". I think this statement is ridiculous, but there is no refutation for dogma. If the universe would be so absurd, I could as well be a christian fundamentalist or just randomly do nonsensical things (since it's all random either way).

As a general rule, arguments which rely on having exhausted the hypothesis space are weak. You can't say, "It can't be algorithms, because algorithms don't solve the problem of the first cause." Well, so what? Neither do the straw men you suggest. Neither, indeed, do "emergence" or "magic", which aren't explanations at all. It's one of those hard problems - it doesn't just trouble positions you disagree with.