In the quantum mechanics or statistical mechanics sense a forbidden event is never completely impossible. Rather it is extremely improbable based upon some symmetry, entropy, or energy constraint. I propose that in most situations time travel into the past is extremely improbable. Theorem: Time travel into the past has an exponentially increasing improbability as changes to the timeline become observable.

Corollary 1: Time travel into the past is allowed if and only if it does not disrupt the timeline.

Corollary 2: The butterfly effect is included in timeline disruptions.

Corollary 3: The butterfly effect does not apply below the level of Heisenberg uncertainty.

Sending a human backwards in time to Earth would create a sudden pressure wave as the air (or water) at that location is displaced. The butterfly effect implies this will always be a forbidden transition.

But a human could be sent to a height where the air pressure is essentially zero then gradually move downward. However it is unlikely that a human could move around and do anything useful without causing sufficient changes to prevent the trip in the first place.

Sending a tiny robot back in time is much more likely to result in no disruptions to the timeline, especially if that robot does little more than float around on air currents and observe.

A time machine will attempt to send a tiny robot back in time hundreds or millions of times per second. Attempt after attempt is rejected by the timeline, but there is a statistical chance of success. After millions or trillions of attempts a delivery vector is found resulting in an identical timeline and the robot is successfully transferred.

Would insertion of a tiny robot into a hurricane result in any changes to the timeline? The minute changes to the air currents at the arrival point could be quickly washed out by the extreme winds in a hurricane. Perhaps the target location with the highest chance of success is the Atlantic ocean during hurricane season.

And how would that robot return to our time? The same way rocks travel forward in time. The robot would find a quiet place and sit there until it is found. It doesn't even need power for that part of its mission. Success only requires non-volatile memory and perhaps a long lived radioisotope to make it easier to find under the detritus of the centuries.

This might mean that a careful search would reveal some of these robots sitting around important places like Jerusalem or Dealey Plaza. But if we found one and decoded the stored media that would change the timeline and wouldn't the trip have been forbidden in the first place?