How do scientists know Iron-60 is created during supernovae?

Don Clayton investigated the production of Fe-60 in his 1971 Nature paper New Prospect for Gamma-Ray-Line Astronomy (paywalled, but the abstract also hints to Arnett & Clayton 1970, also paywalled, but that abstract is unclear as to the contents being about Fe-60). This likely would have used supernova nucleosynthesis calculations (see, for example, Clayton's sometimes collaborator Brad Meyer's NucNet tools, though this is probably more advanced than what Clayton had at his disposal in the 1970's).

Clayton later wrote a summary The Role of Radioactivities in Astrophysics which included a history of gamma-ray lines and discusses the Fe-60:

The $^{60}$Fe nucleus emits a 59 keV gamma ray upon decay, and its daughter $^{60}$Co emits gamma-ray lines of 1.17 and 1.33 MeV. Reasoning that during its long mean lifetime some 50,000 supernovae occur in the Milky Way, their collective effect should be observable. This reasoning applied equally well thirteen years later to the first interstellar radioactivity to be detected, that of $^{26}$Al.

Which mostly confirms the notion that the computations came before the observations (which I'm not sure the Fe-60 $\gamma$-ray line has been observed, Binns et al (2016) indicate that the element itself has been observed in very small numbers as cosmic rays, but it doesn't seem to say anything about the $\gamma$-ray emission).

As always, it depends on what you mean by know/find. As aptly illustrated by Kyle Kanos, theoretical arguments show that $^{60}\mathrm{Fe}$ is naturally produced through stellar nucleosynthesis in the last stages of the life of massive stars, and then injected into the InterStellar Medium (ISM) by SN explosions. This has been known, from a purely theoretical point of view, for a long time, but what is the actual observational evidence?

Also known for a long time is that some radioactive elements are detected in situ, meaning from emission originated within some SN remnants. These include Nickel-56, Cobalt-56, Iron-56,... Recently, even Titanium has been detected in situ, strengthening our belief in the overall correctness of the theoretical picture mentioned by Kyle Kanos.

Iron-60 is trickier, because it is both rare (of order of $10^{-7}$ of the abundance of $^{56}\mathrm{Fe}$) and weak in its emission, so that so far no in situ detection has ever been made. Yet the INTEGRAL telescope has managed to detect the $\gamma$-ray line from its decay. This is an integrated measure over most of the sky, because like I said every source in the Galaxy is likely to be too faint to be detected individually, but their sum produces a cumulative effect that can be observed. This is the best that can be done nowadays.

$^{60}\mathrm{Fe}$ is somewhat similar in importance to the more abundant $\gamma$-ray brilliant isotope $^{26}\mathrm{Al}$. Wikipedia has a good article on it, which may complement what you know about $^{56}\mathrm{Fe}$.