I want to change the format of date from DD/MM/YYYY to DD MMM YYYY in a Modern list. Is there any way to achieve this with column formatting?, we don't want to use calculated column.
I think it's not currently possible to apply custom string formats with column formatting:
As you can see on official documentation, the operators to format dates are:
toLocaleString() toLocaleDateString() toLocaleTimeString()
You can use a calculated column, but if you don't want to use it you can do that with SPFx Field Customizer.
Except calculated column, there is no OOB method that I could thought to achieve your purpose.
Maybe you can do this using code. For using code in modern experience list, as RiccardoGDev mentioned, you should use SPFx.