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According to this answer to When was the last time that Starman/Roadster was seen? it was last seen by Earthlings at least at 2018-03-19 03:22:33 UTC by a 1 meter telescope in South Africa.
Starman will be pretty close to Mars in 2035, so if there is any good Martian telescopes then, they will be able to spot it. We could do so in October of this year, but there aren't any telescopes good enough.
From Earth, January 2047 is the most likely time to spot with a 1 meter or smaller telescope. A 1 meter telescope was what last saw Starman. Because of orbital mechanics, any close approach will happen in the winter with Earth, January to March. The next time it will be close is in 2050, I believe March.
We could spot it with Hubble most of the time, if that was even remotely possible to get time on HST for such a thing, or possibly with some of the really big telescopes earlier, but by far 2047 is the most likely time to get a good image of it.
See also an article that I wrote for Ars Technica, with more similar details.
2018-02-06 and last seen about forty days later. Neglecting angles and the position of the Sun for a minute, when would it be that same distance again?
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