One of the worst fine tuning problems is cosmic inflation. In order for the big bang model to work (to solve the "horizon problem") it requires God/nature to have undergone an extreme deviation in expansion for the perfect fraction of a second, which was suddenly turned on, then suddenly turned off, and any deviation from that would have either caused the universe to near instantly collapse back in on itself under its own gravity, or caused matter to be so spread out that no stars or galaxies could ever form. But typical science communication presents it as just an event in the early universe, not an extreme moment of fine tuning where something turned the dials up and down to the perfect degree for the perfect minute duration, without which no star, let alone life, could exist.

And that's fine tuning after the big bang. Most fine tuning occurs in the extremely small constraints each physical constant requires in order for the possibility of atoms, chemistry, stars, and stellar nucleosynthesis to be possible.