Can I use Rare Candy to evolve a Basic Pokemon into a Stage 2 Pokemon with the "Delta Evolution" Ancient Trait on my first turn or on the Basic Pokemon's first turn in play?
No, you may not.
Source: Roaring Skies FAQ (2015-05-07), TPCi Rules Team (2015-05-07)

Relevant cards

Note: All applicable cards may not be listed below.
XY6_105
XY6_32
XY6_46
XY6_74
XY6_76
XY6_81
XYP_XY57
XYP_XY57
XYP_XY59
XYP_XY59