No – you can advertise one product if you want to, that’s not a problem!
If you only have a handful of products that’s fine. If they don’t change then one way of uploading the into Merchant Center is to use a spreadsheet and upload that directly. If your products don’t change then you don’t have to worry about making constant changes.
There’s no minimum – if you have just one product and you want to advertise on Google then off you go!