Building a buck converter using CMOS 555 with mosfet driver
A 555 seems to be the wrong choice here – either you're building something open-loop, in which case you'll have no feedback and no real regulation, or you're building something closed loop, and then your 555 becomes nothing but an inelegant method to solve a small subproblem of the overal converter problem; you'd simply not do that.
Instead, you'd use one of the many (cheap!) existing buck converter / controller ICs. In your case, the low-power IRL2104 implies that even the very classic ICs will do that at a much lower cost, probability of failure, complexity.
In other words the question &quot;how to build a buck converter with a 555&quot; is as far as I can see answered by  &quot;use the 555 as decoration only, and design a proper buck converter without it&quot;, just as &quot;how do I design an airplane with chocolate pudding&quot; with &quot;use the pudding elsewhere and design the aircraft without pudding. Pudding doesn't help when building aircraft.&quot;
Also, fully aware that you might be subject to availability restrictions, but last time I checked a classic MC34063 (or clone thereof) isn't any more high-tech than a CMOS 555.
To be absolutely clear: if you can buy more modern ICs, don't buy the MC34063. It's really ancient (1983), and voltage converters have progressed a lot in the last four decades; buy something modern, which will have better ripple and regulation, higher efficiency and need a smaller inductor. Using a low-tech MC34063 is just still better than trying to shoe-horn a 555 into the job of a converter controller.