SMPS' bridge diode rectifier before the transformer ?

Why is SMPS' bridge diode rectifier before the transformer which won't/shouldn't work having a DC input ?
Can anyone crystal clearly but succinctly explain how or which is the processes of DC step down ?

Switch mode power supplies run the transformer at high frequency; that's how they achieve good efficiency and small trasnformer size. Depending on the type the internal frequency may be anything from a few KHz up to possibly 1MHz or more in some types, though 50-250KHz is probably the commonest range.

The incoming power is rectified and used to run an electronic power switch that drives the transformer.

The circuit below is an example of a very simple one that does not use integrated circuits, just to show the concept.

The two transistors form an oscillator, with the FET switching power to the transformer at high frequency. The bottom left winding provides an auxiliary siupply to run the oscillator (and provide a "bootstrap" function by th elook of it, in this design).

The right-hand winding is for the power out of the PSU. It's regulated by the optoisolator starting to conduct and change the osillator bias when the output boltage is in the correct range.