Multiple Voltages Needed - Can I Simply Cascade Power Supplies?
Cascading supplies does guarantee that they come up in order but you can't do it in your specific case.

The minimum input voltage for the LM2576 is between 3V and 4V depending on temperature.
https://www.onsemi.com/pub/Collateral/LM2576-D.PDF

(See figure 11 on page 6 of datasheet)

Therefore you can go from 12V to 5V to 3.3V.

The 2.5V supply may or may not be able to run from 3.3V. 

The 1.8V supply probably won't be able to run off of 2.5V.

If you want to sequence the supplies by running one off of the other then you need to pick a supply that has a minimum input voltage that goes all the way down to 2.5V.

Also it should be noted that the overall efficiency goes way down if you cascade so many supplies.  For example if each of your supplies was 90% efficient then...
You get 12V at 90% efficiency.
You get 5V at 90% of 90% = 81% efficiency.
You get 3.3V at 90% of 81% = 73% efficiency.
You get 2.5V at 90% of 73% = 65% efficiency.
You get 1.8V at 90% of 65% = 59% efficiency.
And so on...

A better way to sequence the supplies and obtain high efficiency is to run them all off of 12V, but control the ON/OFF pin of each supply from the output of the other supplies.







simulate this circuit &ndash; Schematic created using CircuitLab