The challenge for us now is we may not have the breakthrough that leads to the invention that leads to new way of thinking that allows time travel.
Imagine explaining nuclear fusion to a mind that hasn't experienced steam or fossil fuels. My point is on "ever possible" it is too early to say as I am of the mind that humanity still has long ways to go technologically.
If I were to speculate I'd say the following.
1. Traveling forward seems most likely due to relativity of a person or object in a device and those outside. Think of it like stasis.
2. Fixed points creating a loop so time travel would be possible at a certain point far in the future.
3. Time Lord travel in a Tardis going where ever you want...this sadly seems very unlikely and as others have touched on could destroy reality.
