How do I procure SoCs in small quantities?
You really have to consider the application as there such a broad range and there is an equally broad range of SOCs to apply.

Take for example the STM32F76x series. That could easily be considered to be an SOC with the sheer number of circuit subsystems on it including on board FLASH and RAM.

Or consider another example the Intel C3000 series processor family. The series supports up to 16 64-bit cores and high speed I/O lanes that can be used for SATA, PCIe or USB.

Both of these SOCs have family members that can be purchased in single lot quantities from Mouser.