It is not possible. In addition to the missing socket, there are other components missing, some are under the shield.
Care to elaborate? Not much should be required, so this is a bit surprising, unless it's an intentional disabling.
That said, USB-based storage could be another option - but it should be kept in mind that neither is robust in the face of unexpected shutdowns/reboots - one of the real strengths of these platforms over the computationally far more powerful and hardly more expensive raspberry pi, is that they don't depend on a fragile SD card. If you could boot a pi W from an SPI flash, it's questionable if there would be a market for MT7688 systems at all.