What is the basis of your conclusion the uP is not powering up ? (EXACTLY HOW did you come to this conclusion ?) What observations was that conclusion based on ? The ATmega328 doesn't have any specific output pin that would indicate that it has powered up except D13 if you run the Blink Example.
I see no led connected to D13 and you have not said anything about testing the chip with that sketch so we can assume you have not done so. Remove everything else from the ATmega328, connect a led with a resistor to d13 and run the Blink Example.
Your post is inadaquate to deduce the nature of your problem for the following reasons:
1- as posted, it can be assumed this is your first standalone ATmega328 circuit so we cannot assume you actually know what is necessary to get it to work. On the face of it, everything appears 'ok' , but on close inspection
2-no values are given for the crystal caps.
3- No part number is given for the crystal. We can assume nothing about a 'Newbie' post for such a circuit. Everything could be wrong.
4-There is no FTDI interface shown and it obviously cannot communicate with the IDE without it . Nothing has been stated about how you program it and as shown, it could not be programmed (sketch uploaded) without an FTDI interface.
5-The OLED interface is incomplete (the only connection shown is A4 & A5 , which suggests it is an I2C device. No power connections are shown and no power consumption specs are given.
6-No output voltage is given for the regulator
7-No DTR to RESET pin cap is shown,
8- Your post is for an ATmega328 issue but your schematic shows multiple other devices.
If you are posting for an ATmega328 issue, remove everything except the ATmega328 and then we can say with certainty that it is indeed an ATmega328 issue.
9-You have not posted your code. (use the IDE Blink Example to rule out code as cause of problem)
Remove all connections to other devices.
Measure the regulator output voltage
Measure the total current drawn from the regulator using a DMM.
Post the crystal cap values
Post the crystal part number (and vendor link if possible)
Explain how you are uploading sketches (no connection is shown to the Rx & Tx pins) (is there an FTDI ?)
There is no information to suggest the problem is related to a cap.
Do you have an arduino UNO ?
If so , test the standalone ATmega328 (after disconnecting all other devices) using the 5V from the UNO instead of your battery/regulator.
I am not good with electronics but it sounds like a cap problem
State your reasons for this conclusion.
Where did you get the ATmega328 chip ? Did it come with the bootloader ?
I currently have 4 standalone ATmega328 circuits breadboarded and none of them have ever exhibited this symptom. Did you test it with the Blink Example BEFORE you added all the other devices ?
Did you then (after verifying it worked initially with the Blink Example with no other devices) THEN add ONLY ONE device and retest it with the blink example and then after verifying it worked with the one added device, add ANOTHER device and RETEST it with the blink example and so forth until all of the devices (OLED, NRF24L01,DHT,DS18B20) were connected ?
Did you read this before breadboarding your ATmega328 ?