Is it possible to simplify 555 delay circuit?

It depends on your desired trigger signal characteristics, such as high going, low going, do you want it level triggered or edge triggered, pulse amplitude and duration, and maybe more. Then there’s the output, do you want it to go high or low during the on period, what do you need it to drive, etc.

Typically for a 555 monostable delay the output will be held near ground and on a low going pulse on the trigger pin going below Vcc/3 the output will go high, ~ Vcc-1.7V, for the time determined by the timing resistor and cap. When the cap charges up to 2/3 Vcc the circuit will reset and the output will return to its liw state until triggered again.

The output high and low currents available are not necessarily equal, and this depends on the exact type of 555, ie. CMOS, bipolar, etc. The datasheets are your friends, make sure you have the one that matches the 555 version you are using.

From the red input to the blue output, the net effect of the overall circuit is delayed inversion. In its most simple form, all of the active components can be replaced with one diode and one inverting device such as a transistor or 1/6 of a CMOS hex inverter. A real-world solution probably needs more than that, such as three inverters in series, but we just don't know . . .

If you want to stick with a 555, then Yes, both logic inverters can be replaced with one diode. The 555 is acting as an inverter with hysteresis.

I had this answer almost ready to post and was called away, so Carl beat me to it. I started with his version, then opted for this version wherein the capacitor discharge timing is not affected by the input source output impedance or low output voltage value. His 555 Threshold input connection is interesting.