There is nothing particularly special between ATTiny88 from the rest of old generation of ATtiny chips or ATMega chips in terms of programming the chip without a bootloader. While the bootloader such as the Optiboot used by many Arduino boards allows program to be uploaded to the chip via USB or UART interface, to program an AVR chip without bootloader, you need an ICSP programmer to program via the so-called ICSP port which as you can see from the provided Wikipedia link is basically an SPI interface.
The good news is that even you don't have a dedicated ICSP programmer, you can turn an Arduino UNO or Nano into a programmer. You only have to do one thing:
Upload the ArduinoISP sketch to the Arduino UNO/Nano board that will serve as the programmer. You can find the sketch in the Arduino IDE under File → Examples → Built-In Examples → ArduinoISP.
This answer provides additional details that you would need to program the ATtiny88 using ICSP.
If you are using the ATtinyCore as your ATtiny88 development environment, there are options for you to select whether you want to program the ATtiny88 with or without the bootloader.
