Hi @solonofathens ,
I'm wondering if you got a model with the eMMC storage that is soldered directly onto the motherboard as there seems to be a lot of different motherboards available for the model.
You may have to [https://pcsupport.lenovo.com/au/en/products/laptops-and-netbooks/100-series/120s-14iap|enter the serial number] and find out the specifications for your exact motherboard variant. (see Item #4 p.73 of the hardware manual) as some that I searched for had either 32GB eMMC or 64GB eMMC flash storage hard mounted and therefore maybe there is no M.2 slot provided.
What capacity SSD is installed now or what capacity is the storage in the laptop?
On p.66 (see also p.74) Item #7 in the [https://download.lenovo.com/consumer/mobiles_pub/ideapad120s-11iap_120s-14iap_hmm_201707.pdf|hardware maintenance manual] it shows the ''minimum'' SSD capacity which may already be installed is 128GB depending perhaps on which motherboard you have.