I need to make my program run immediately on a reset or power up. However, the bootloader delays program startup by around 2.5 seconds. How can I get over this? Is there a way to turn off the bootloader wait period?
Yes. You remove the bootloader completely and program the Arduino using a hardware programmer.
If you could "turn off" the wait period you would never be able to get into the bootloader to program the board, so the bootloader would be completely useless. So either way you would then need a hardware programmer to do anything constructive with the board.
A hardware programmer could be another Arduino, or a real hardware programming adapter.