Can I use atmega328P without capacitors?
Those specific capacitors form part of the resonant clock oscillator circuit. If you are using a quartz crystal then they are required. You can't do without them.

If you use a 16MHz ceramic resonator, however, they don't need the capacitors (they're built into the resonator).

Also, if you have your ATMega328P on a breadboard the capacitance of the board itself is sometimes enough to "get it working", though as soon as you transfer your circuit to a permanent PCB it will suddenly stop working for no apparent reason.