Aristarchus gives a calculation which would result in a value for the Earth-Sun distance of about 0.016-0.065 au; clearly, that's a long way out. The true value is 1.00 au.
Archimedes gives a value that would correspond to 0.43 au; other ancient authors gave a range of values, all less than 0.5 au, and many were close to Aristarchus's value. So, among ancient writers, all we can really say is that "They had no idea how far the sun was."
Kepler and his laws of planetary motion could show that values of 0.02 au were far too small (since then a very significant parallax would be visible in Venus) but couldn't say with precision how far out.
In the 17th century, telescopic measurements of the Earth-Sun-Moon angle allowed for Aristarchus's method to be used with greater precision and yielded values of 0.5 au or more.
Huygens made a number of assumptions on the size of the planets and came up with a very good value of 1.068 au, but his reasoning was faulty. This value is more luck than good maths. However, Cassini used observations of Martian parallax (and a good estimate of the size of the Earth) to get a well-calculated value of 0.925 au.
This was the best estimate prior to the measurement using transit of Venus.