This challenge is not going to display real time tracking.
It will unlock after the completion time ends.
This may be retroactive like the previous challenge and so you won't need to play the game at all and still get it. (However I advise you to play one match at the very least just in case.)
Fastest possible way to make sure you get credit for this:
Launch any mode (campaign or practice match are advised) and then draw your intiial hand of cards (not sure if that counts towards total) and then wait for your first turn to start, right after you draw the card press start and concede.
If the challenge is starting from scratch I don't think any of us need to grind for it but if for whatever reason you want to, I suggest building a blue deck.
Effects that add cards from your deck directly to your hand/field/discard pile/etc. probably won't count for this, use cards that tell you to "draw".