To recap: in our current state, time travel does not appear to exist naturally except in thought patterns and memory. When time travel is discovered (probably soon after the variableness of the speed of light is understood), travel to any point into the future becomes possible, since both start and end points would have a rooted verifiable reference (such as a custom wormhole).

Travel to the past, if possible, could only occur back to when time travel was first discovered; prior to that, there is not yet a first fixed position to make it possible for time travelers to be here now: there will be no reference point to go back to until time travel is invented.

Pop paradoxes such as the Grandfather Paradox become irrelevant (or at least they are for anyone born before the discovery of time travel).

Much like the singularity shakes, inventing time travel could change the universe so drastically that it may become hostile to life; the future of a universe with us in it may depend on how long this “flip” takes to happen. If there is any time at all from when time travel is discovered to when the universe becomes non-life supporting, then the resemblance of humanity and any other pansentients may be able to exist in the event, assuming sufficient time engineering skills are available and that the event duration occurs in the first place. If it takes no time at all to change from time tavel reference 00000000 to an uninhabitle space-time universe, then we may well all be stuffed.

A controllable event with both space and time resources would become the most valuable resource in the universe, across all sentients. No matter the volume or duration, provided there is some time to contain an engineered solution it should be possible to maintain life (in some form or another).