Sandbox means that you can do whatever you want to your site, ie. publish content like crazy, build links, remove / edit the content, drive real traffic to your site, have great products and services that make billions of people buying them everyday, etc... you can do any, or all of these things and literally have the best, most useful, and most important site in the entire Universe and google won't give shit about it. They'll refuse to rank it during the first months / years of its existence. Why do they refuse to index such a gem of a site? Nobody knows (except for google, obviously). But the point is that they put your site in a sandbox where you can play with it without affecting anything. That's the sandbox...
Also, the thing with 6 months that you mentioned is the norm / average, but it's not always 6 months. Some sites stay in the sandbox for 1-3 months, others for 1-2 years or more... You can't know this until you start ranking all of a sudden without knowing why. This has happened to 2 of my sites back in 2020. I purchased 2 sites in September 2020 and did nothing to them because I was busy with other projects.
I just added both sites to my GSC and then let them sit there (and they were bad sites, too by the way, each one having only 10 articles of 400-500 words that were badly written... even the site design was bad)... so anyway, I added those 2 sites to my GSC like I said, and then I forgot about them until last year when I noticed they started getting impressions in GSC on the same day of the same month.
So, 9 months later they have both started getting daily impressions, those bad looking sites (2 different niches, by the way) with gibberish content that nobody cared about for 9 months all of a sudden showed up in google's index on the same day of the same month, huh? Pretty big coincidence if you asked me

... But it wasn't coincidence, it was just the sandbox....
EDIT: if your site is indexed and at least getting impressions you can start building links... well, to the indexed pages anyway, otherwise it looks suspicious to google that people link to pages that don't exist (in their index)