The SPI(SCB) PDL has APIs for writing the data. You can straight away use the existing API to transfer the data instead of implementing the function yourself. For example if you want to transfer the data to the SPI slave you can use the following API:
Please refer to PSoC 6 Peripheral driver Library: PSoC 6 Peripheral Driver Library: SPI (SCB) which mentions all details about using the SPI component. You can refer to the code snippets for configuring the SPI in the beginning.
You can also refer to the following code example that demonstrates the use of SPI SCB (Serial Communication Block) Component for PSoC® 6 MCU in master mode: https://www.cypress.com/documentation/code-examples/ce221120-psoc-6-mcu-spi-master
Kindly let me know if you have any further queries related to this.
I believe the reason that Seegar (the creators of the EmWin) library did not provide an initialization routine is that depending on the display IC involved (eg. the ST7789, ST7735, etc) these init commands might be different. This includes your application specific setup like the screen size (eg 240x320 pixels) and display orientation (eq Portrait or Landscape).
As Ekta indicated using the Cypress SPI APIs are best if you can use them. It does the hard work of the HAL (HW Abstraction Layer) calls to the actual PSoC registers.