No. We are stuck in our own personal current times. Time is defined by on-going events. As the events of the past are done deals, there is no time in the past. As the events of the future are yet to unfold, there is no time in the future. We cannot go beyond our own personal time, the current, because there is...
The sun warms us.
Without it, the Earth would freeze to about 3 degrees Kelvin (minus 270 C)
No life on earth would survive.
The moon gives us some light at night and contributes about 50% of the ocean tides (the sun contributes the other 50%. If the moon just disappeared, the earth's orbit around the sun...
186,000 miles per second
186,000 x 365 x 24 x 60 x 60 miles per year
= 5865696000000 (using my calculator
= 5.865696 x 10^12 miles/year
But it is possible.
The main objection is that we have not yet been visited by a traveler from the future. And assuming time travel becomes possible in the future - then time travel would happen to the past (our present).
Another objection is "how would we know:.
If someone traveled back to 1920 and...
Doubt they exist. I once met Betty Hill. Not a believable source
The best reason would be to shield a radio observatory from the very noisy Earth...
And "Dark side" doesn't mean that there's no light - it was referred to as 'dark' in that we had no information about the far side (until the Russians did the first fly-by in 1959).