`Instant::PAST_VALUE` constant?
One potential problem I can foresee is that because this is loosely defined (there are many possible values that all work), it might cause compatibility problems going forwards (where we might have a reason to change it from one value to a different value, but that might break existing code that is, e.g., using it as a sentinel), or where it's used as a sentinel on one platform and then an attempt is made to read it from a different platform where the value is different (although Instant is already platform-specific enough that such code would already likely be broken, so maybe that isn't an issue).
I assume that the reason why you want this rather than just using Instant::now() is so that it can be a compile-time constant? (Guaranteeing that an Instant is strictly in the past is difficult due to the possibility of a Rust program running during very early boot, before the timestamp has had a chance to change from its minimum value.)
Discussion in the ATmosphere