Are those "USB-C" SSDs using the Thunderbolt protocol? Check the icon next to the USB-C port on the SSD and your SSD's product documentation & user guide to see which protocol(s) the SSD supports. Unless you purchased a Thunderbolt SSD, the SSD you have will most likely only support the USB protocol.
If there is a lightning bolt symbol next the the SSD's USB-C port, then it supports the Thunderbolt protocol.
If there is a trident symbol next to the USB-C port (may be sideways), then it indicates the drive uses the USB protocol.
If there is no symbol or markings next to the USB-C port on the SSD, then assume the worst and it only supports the USB protocol. However, you should review the SSD's user manual to be certain.
USB-C is very confusing. USB-C is actually a connector type...that is all it indicates.
Both the USB3/4 protocol & Thunderbolt 3/4 protocol now utilize the USB-C connector. Plus some USB-C ports on devices, may not support any data transfers at all and may only be used for power. Users must careful read & understand the product documentation for their devices which utilize a USB-C connector (this even includes cables since some cables may only transfer power, while others may only transfer using USB protocol at very slow USB2 speeds). You cannot always rely on the marketing materials as they will hype up keywords which may not really apply to the product in order to mislead people.
If the SSD supports the Thunderbolt protocol, then you can use an Apple Thunderbolt USB-C to Thunderbolt 2 Adapter to connect the drive to an older Mac, but the drive will likely run much slower than it would if connected to a newer Mac with Thunderbolt 3 ports.
If the SSD supports the USB protocol, then you can use an Apple USB-C to USB-A Adapter to connect the SSD to an older Mac's USB ports. Again, depending on the speed of the SSD, it may run slower on the older Mac since the USB speeds on older Macs generally is limited to 5Gb/s.