**Abstract:**

Testing the variation of fundamental constants of Nature can provide valuable insights into new physics scenarios. While many constraints have been derived for Standard Model coupling constants and masses, the $\theta$ parameter of QCD has often been ignored in these studies. This letter discusses potentially promising paths to investigate the time dependence of the $\theta$ parameter. While laboratory searches for CP-violating signals of $\theta$ yield the most robust bounds on today's value of $\theta$, we show that CP-conserving effects provide constraints on the variation of $\theta$ over cosmological time scales. We find no significant evidence for a variation of $\theta$ except for a mild hint around $z\sim 4$ which would imply an ``iron-deficient" Universe at high redshifts. Finally, we also sketch an axion model which results in a varying $\theta$ and could lead to excess diffuse gamma ray background, from decays of axions produced in high redshift supernova explosions.