Can I use Cinccino's "Make Do" Ability to discard a card, then do other game actions such as play a Cynthia, and then finally draw the two cards later in my turn?
That's not how it works. You have to perform all of the actions of the Ability before moving on to other game actions.
Source: Sword & Shield FAQ (2020-01-24), TPCi Rules Team (2020-02-06)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH1_147
SWSH1_147
SWSHP_SWSH009
SWSHP_SWSH009