I am using vs code on Mac and I am a CJK user. Ctrl+Space is a shortcut for switching IMEs on my Mac.
If you open the keyboard shortcut pane (just press Command + K, then followed by Command+S), then search for trigger suggest, you will find that there are actually two shortcuts for this function:
So in case Ctrl + Space is taken by other programs. You can use Option + Esc to trigger suggestions. If you are using a Windows keyboard, Option key is Alt. You can also change the keybindings for this command as suggested by @Atilla Baspinar.