Programming standalone Atmega328p-PU with NE555N timer IC
The default configuration of these chips, as they come from the factory,
is to use their internal 8 MHz RC oscillator downscaled at 1 MHz. So you
do not need any extra oscillator to program them.

Once you program the chip the first time, if you configure it to use
an external resonator/oscillator, then you do need to have that
attached in order to reprogram the chip.

A 555 may be able to run the chip, but if you want to reprogram it, the
programmer may not cope well with the extra-low frequency the chip would
be running at.