I am in the same boat, got the invitation last week and tried to appear for the test today (i.e. after the start date/time) but getting the error message:
You can’t take the test right now. Based on our records, we haven’t invited you to take this test right now.
I contacted IRCC via email and it may take days before they respond. I called IRCC too and they suggested me to wait for the response. I guess I can't do much, took the couple of days off from work for preparation but will have to prepare again as its difficult to remember especially the historical dates / names.
The worst part is that when I prepare next time and try to appear for test, the same issue may happen at the Sign-in to get the Test Link.