Is it possible to convert SPI to UART without a microcontroller?
Yes, if the SPI bit rate matches the UART bit rate you want to generate, it can be done.

The SPI data stream needs to be carefully constructed:


SPI data is normally MSB-first, but UART data is normally LSB-first, so you'll need to reverse the bit order in each of the data bytes.
UART data contains a start bit and a stop bit bracketing each byte, so for each 8-bit data byte you want to transmit, you need to put (at least) 10 bits into the SPI data stream. One easy (but inefficient) way to do this would be to alternate data bytes with bytes of 11111110.