Google has a history of not letting its search suggestions play nice with non-Google products, so this may break at some point. However, the following settings should let you use search suggestions with the google search engine in Vivaldi. (Works for me in Vivaldi 5.5.2770.3.)
Firstly, make sure search suggestions are turned on in settings (vivaldi://settings/search/) for the address field or the search field, depending on where you want to use it. Based on your privacy preferences, optionally check the "Only when using search engine nickname" box.

Next, paste the following URL into the "Suggest URL" field for your google search: https://www.google.com/complete/search?client=chrome&q=%s
Mine looks like this (but I use the .com.au URL elsewhere, yours may be different):

Once that's done, you can use the keyword search using the search engine's nickname, e.g. "g vivaldi google search suggestions", to search with suggestions enabled.
If you're not worried about privacy, you could try leaving the "only when using search engine nickname" field unchecked, and it should work without the "g" at the beginning.