How can good outcomes, and not just trade-offs, be achieved through economic policy?
This is impossible since there is no agreement on what is a good outcome. There is no policy that maximizes every single welfare criterion (e.g. Rawls Max-Min, Utilitarianism, libertarian criterion, charitable libertarian criterion, etc).
For example, not everyone might agree lowering inflation is 'good'. It depends on what sort of welfare function you pick and as a result tradeoffs are fundamentally inevitable, even when there are Pareto improvements since perhaps that pareto improvement results in less (or heck even more) equal distribution than prescribed under some social welfare function.
Take the tradeoff between inflation and unemployment as another example. It is impossible to have both low unemployment and low inflation. One of the 2 will always be uncomfortably high.
This is not necessarily true. First, inflation can be low simultaneously with unemployment being low. For example, consider standard Philips Curve given by:
$$\pi - \pi_e = - \alpha (u_t-u_n) \tag{*}$$
where $\pi$ is inflation, subscript $e$ indicates expectations and $u_t$ and $u_n$ are the actual and natural rate of unemployment respectively.
The Philips Curve above describes the inflation unemployment trade-off since the more $\pi$ is above $\pi_e$ the lower the unemployment. However, this trade-off does not mean you can't have low inflation and low unemployment. Parameters $\pi =2\%, \pi_e= 2\%, \alpha =1, u_n = 1\%$ will give you unemployment rate of 1%. This is such a low unemployment rate that any politician would brag about it, yet with this 1% unemployment rate inflation is 0%.
The inflation unemployment trade-off just means that to bring unemployment lower than its natural level you need to produce inflation that is higher than expected inflation. Or conversely, to lower the inflation you need to bring unemployment below its natural rate. That is the trade-off. However, combinations of low, low; high, low; low, high; high, high inflation and unemployment respectively are all possible depending on economy's parameters.
It seems as though the solution to any problem comes with its own equally bad set of problems. At this point, the question arises as to why we bother with economic policy at all.
This is sort of like asking why try to plan vacation if there isn't a perfect vacation destination because any place will have at least some negatives and any place will have at least some positives. Just because there are trade-offs it does not mean the smart thing to do is just throw dart on a board and end up somewhere in malaria ridden jungle.
The ideal of science based policy is to enumerate trade-offs for public (e.g. for 0.5% extra inflation we can lower unemployment by 0.3% etc) and then it is up to public to decide what is more important to them.
For example, in US people vote for congress, and congress decided to set up Fed with mandate that it should try to keep some balance between low inflation and high unemployment. In EU people elected their heads of state that signed treaty of Amsterdam giving ECB mandate to keep inflation low regardless of unemployment, because the representatives they elected cared more about price stability than employment.
The purpose of monetary policy is to manage inflation in such way that these objectives are followed. If there would be no monetary policy then people might end up with outcome they don't like (e.g. Europeans with high inflation but low unemployment).
I can think of 2 theories that would resolve this. The first is that there is some optimal outcome for the economy, some optimal and possible level of economic growth, inflation, unemployment, etc, and we keep swinging back and forward past it, unable to hit it accurately due to the coarse-grained nature of control a government can achieve through economic policy. The second theory is that the optimal economic state varies over time, due to societal and technological factors, and so the purpose of economic policy is to chase that varying state.
First of all I wouldn't call this theory since in science that word has more specific meaning, but regarding the arguments:
Given some social welfare function (e.g. Rawlsian Max-Min, Utilitarian, Marshallian etc). There will always be some optimal level of growth, inflation, unemployment and whatnot. The problem is that you still face a trade-off between these social welfare functions. That trade-off cannot be eliminated.
You are also correct in postulating that IRL government never can precisely hit these optimal values, even if government selects lets say Rawlsian Max-Min criterion. This is just because of uncertainty, limited set of tools etc. Government is not omnipresent and omnipotent. Moreover, governments are not completely benevolent either, even in well developed democracies politicians sometimes pursue self interest at an expense of public interest (e.g. see discussions across Muller Public Choice III).
Regarding the second 'theory'; again the observations are not incorrect. Once you select the social welfare function there is some optimal value for each parameter, and this optimal value will constantly change due to state of economy changing as it is perturbed by shocks such as new technology.
However, incorrect part in your arguments is to assume that there is some the optimal value. There are various optimal values corresponding to various social welfare functions. Social welfare functions are derived from moral philosophy. There is no agreement on a moral philosophy that would be 'uber alles'. Even if we discard all unpleasant moral philosophies such as let's old Norse moral philosophy where raping and pillaging was ok as long as it was not done to other members of a tribe, you are still left with a plethora of moral philosophies that are widely considered palatable in modern democracies (e.g. philosophies based on Rawls, Nozik, Bentham, Aristotle and so on).