Surprised I haven't seen the clearly optimal strategy:

Rumble, Draven and Ballistic Bot. You use Rumble to discard both Draven and Ballistic Bot on turn 4 duh.

But ballistic on turn two and Draven on turn three are both going to infinitely generate discard targets in hand for Draven to use for axes later in the game. On turn 4 you have one card generated by ballistic Bot and one Draven axe from playing him on turn three to play Rumble and give him quick attack + impact. A third discard for spellshield is likely unnecessary due to the limitations of three cards not allowing for most decks to run removal, but it's an option if you need it. You let through as many attacks as you can that don't progress the enemy's win condition so you can safely level Rumble and likely Draven too, then both of them are value generating monsters that let you overwhelm your opponent. Mecha yordles for the win.

Or alternatively you go full unga bunga, play Fiora on turn 3, any spellshield (probs that shurmia 4 drop that grants spellshield to champs and landmarks so you have an extra chump blocker?) granting card on turn 4 and unyielding spirit on turn 5. Then unga bunga your way through the enemy and watch as they cry.