Can I upgrade the SSD drive in Mac Mini M1?

Can people buy 256 SSD Mac Mini M1 and upgrade it later, or can't upgrade it like memory?

Both the memory and the SDD are not upgradable. Storage can be expanded by adding an external drive. Apple specifications state the internal drive has speeds up to 3.4 GB/s. Samsung specifications state the X5 Thunderbolt 3 SSD has speeds up to 2.8 GB/s. So storage can be expanded by adding an external Samsung X5 drive, albeit at a 18% drop in speed.

I am using a 2018 Mac mini with a 256 GB internal SSD. I quickly learned this was not enough storage. A 500 GB Samsung X5 SSD was added. The Mac was configured so macOS resided on the internal drive while the each user's home folder resided on the Samsung X5 drive. This allowed macOS to operate a maximum speed, while there was sight drop in speed when accessing user files.

Note: The Samsung X5 drive has TRIM support when used with macOS.

I should point out that at the time of purchase you can upgrade the 2020 Mac mini to an internal 1 TB SSD for $400. Samsung's list price for a 1 TB X5 SSD is also $400.

A user's home folder location can be set from the User & Groups pane of the System Preferences application. See the article Move Your Mac's Home Folder to a New Location.