Astrophysics is kind of in the same boat. You can't really set up a proper test and control - you're forced to do what you can with the datasets that are available.
As W. Brian Arthur has observed, vrtually all of economics ultimately boils down to questions of policy. There is effectively no theoretical (as opposed to policy-oriented) economics, let alone a truly experimental sort. This applies not just to orthodoxy, but many heterodoxies as well.
The notion that science is of necessity experimental is fundamentally false. Experiments are useful, but the core of science is that it is observational, you might call it experiential, with hypotheses and observational tests (of which experiments are one subclass) being used to form theories and models.
The scope of, say, experimental cosmology, meterology, geology, paleontology, evolutionary biology, and ecology are ... fairly small. Though not entirely nonexistent. Famous proofs, or validations, of Einsteins theory of general relativity were observational, based on star positions during solar eclipses and of Mercury's orbit. Neither of which lend themselves readily to laboratory experiments.
Similarly, simulations are a powerful tool in many disciplines.
Geology is an interesting case on several counts.
It's among the oldest of the natural sciences, dating back thousands of years, to at least ancient Greece (Theophrastus, 372–287 BCE, Peri Lithon). It has been almost entirely observational, rather than experimental. As recently as the late 18th century, the Earth was thoght to be unknowably old (James Hutton, I believe), and through the 20th, informed and scientific views differed by orders of magnitude. It wasn't until the 1st decade of the 20th century that early radiometric dating suggested even approximately the right range. The actual. value, plus or minus 1%, wasn't determined until the 1950s. And the central organising principle of a study dating back 2,400 years wasn't. finally accepted until 1965, having been proposed in modern form in 1912. That is, it's only 55 of 2,200+ years that geologists have formally had the foggiest notion of how their study actually works.
And even. still, in one major application, earthquake prediction, the field remains conspicuously incapable, at least where timing is concerned. Criminally so according to Italian courts: https://www.scientificamerican.com/article/italian-scientist...
We've an exceptionally good idea of where earth movements are likely to occur, what landforms are especially vulnerable, and what construction methods most resilient. But precise timing eludes us -- at human scales events are effectively random.
Economics prides itself on its reliance on maths, dating to Alfred Marshall, to which I can only commend this Reddit thread:
https://old.reddit.com/r/AskEconomics/comments/bevb7u/why_is...
Economics, my own course of academic study, remains mired in wishful thinking, false models, self-serving theory, and rejection and suppression of well-grounded alternative or additional concepts. It specifically rejects thermodynamics (Georgescu-Roegen, Daly, Ayres, Hall, Keen, and others), evolution (Veblen), complexity (Arthur and others), and limits (John Stuart Mill, William Stanley Jevons, Kenneth Boulding, Meadows et al, and others). Even where at leaast some elements of the mainstream have resumed rational behaviour, policy and public discourse frequently have not.
Epistemic progress and ideology are all but incompatible. If not entirely. Until economics entirely rejects ideology it will not progress. Given its foundations in moral philosophy and the inherent self-serving dynamics of wealth -- "Wealth, as Mr Hobbes says is power" notes Smith. in one of the shortest and clearest sentences of Wealth of Nations, a book generally given to neither -- this seems a formidable challenge.