I checked all the settings available in the VSCode settings for me, and I don't think there is a way to do this.
There are some settings related to the fact that the VSTode is a window into which folders will be opened, but nothing similar to the Sublime Text setting remember_open_files .
The closest I found is to run code --user-data-dir . (feel free to replace it with some other directory so that you don't pollute your current working directory) from the terminal to indicate that VSCode should not remember ANY previous settings, but that seems redundant for what you are trying to do (as VSCode will start literally as if it was the first time it started after a new installation).
EDIT : I just found the View: Close All Editors command in the command palette (CMD + SHIFT + P). The shortcut for OSX is CMD + K, CMD + W , and this will close all the files that you opened!
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