So, if you need no timing delay, they all you want is to control the brightness of a LED based on an analog input signal.
This is what BJTs are for.
Get a 2N2222, a suitable base current resistor, and a suitable collector current limiting resistor, and you should be golden.
I'd start with a 10 kOhm base resistor and a 470 ohm collector/LED resistor, and tune from there.