Loki (2021)

[Rakaydos]

Again though, they can notice and remove a timeline if someone is late for work when the timekeepers didn't say they would be.

The TVA only don't notice things if any changes are immediately undone, eg. by an apocalyptic event.

Remember that they are absolutely, fantatically, pathologically driven to prevent the emergence of a multiverse. And again, just look at the language they use among themselves. The Sacred Timeline. That's not a descriptor you use if there's any amount of "close enough".

Their entire organisation is dedicated to the preservation of one, uno, a singular version of any event which could ever possibly have happened. The only times things can deviate is when everything present is erased immediately anyway, which is exactly what they would have done with it.

Loki literally went thousands of years without realizing he was anything but Asguardian. Thats an absurdly long time between Frigga making a variation, and it having any affect on the timeline... which is WHY they get so many loki variants. The TVA couldnt tell Young-Loki-but-secretly-IceGiant apart from Young-Loki-but-secretly-Troll until troll does something off-script, and cant detect any "variance energy" unless things start changing from the sacred timeline.

Edit: We also know that "the timekeepers are paying close attention to every aspect of this case", implying that they sometimes dont pay all that close attention at all. At this point we can assume Loki's adoption was poorly monitored.