Yes, fine-tuning is puzzling... I will take the particle physics part in my discussion below.

Fine-tuning is so puzzling that it consists (actually, naturalness to be precise) in one of the guiding principles paving the development of theories extending the Standard Model of particle physics. We indeed have strong hints showing that the Standard Model is an effective theory originating from a more fundamental one to be discovered. In this more general theory, the 26 parameters of the Standard Model could find a nice less fine-tuned explanation.

So, there is still a lot to be discovered, current models have pros and cons. But there are models very useful in the meantime we discover something more fundamental. This by no mean means we will never be able to explain something without invoking some god...