To underline this point: we shot a red tesla into space about 2 years ago [1]. We cannot detect it any more. We'd need a telescope with a mirror of 15km to see it. Due to uncertainties accumulating, even if we'd had a scope like that, we'd probably not be able to point it exactly enough.

Oh, and that thing is mostly between the orbits of Mars and earth - much smaller search space than "the entire solar system"

[1] https://www.whereisroadster.com/