Question about custom domains when publishing a site (developer platform)

Site URL: https://crimson-eagle-f2t2.squarespace.com/

The reason for my question is this: my work blocks newly registered domains, but the website needs to be viewed at work since it's intended for an upcoming work-related event.

So right now, you can access the defaultfreenamesite.squarespace.com URL fine at work. Additionally, I transferred the intended domain name to the site, but that one's blocked at work since it's new. So to be clear, the site has two URLs to access it from, the free one and the one I bought separately and transferred to the squarespace site—the latter is not accessible from work.

Due to this, I'm considering just buying a domain through squarespace for this site, and using that when I publish the site. My question therefore is: would this new domain from squarespace be considered "newly registered" or whatever (domains newer than 60 days or something like that)? And if it is, would I still be able to access the site at work via the original default free URL (the xxxxxxxx.squarespace.com one)? And regardless of that outcome, would the site still be accessible by me at home (and at work if I can get it unblocked) at the second domain described in the second paragraph above?

When you connect to a primary domain (eg abc.com), the built-in domain (xyz.squarespace.com) will still work.