much of science is based on engineering that made it work
Engineering is a form of applied science. This is why it is vital that engineers understand the laws of physics, and particularly the laws of Newtonian mechanics. You can't be an engineer without understanding how forces work.
In general, theory comes before application. Science comes before engineering. It's not the other way around, as you believe. Engineers don't just magically build stuff that works, and then invite scientists to have a look to work out how they did it. This is why, for example, no-one built a Tesla car in medieval times. Engineering is based on science.
science [...] doesn't work.
Scientific theories are falsifiable, yes, that's a fundamental strength that sets it apart from, say, religion. If the theory doesn't work in practice, that simply adds to our understanding, and helps scientists to devise new, better theories. If it does work, then it is reproducible, and anyone with sufficient expertise can verify this.