Once Oblivious Bookworm's ability begins to resolve, it's too late to put any permanents onto the battlefield face down under your control or turn any permanents face up to prevent yourself from having to discard a card if you choose to draw a card.
At the beginning of your end step, you may draw a card. If you do, discard a card unless a permanent entered the battlefield face down under your control this turn or you turned a permanent face up this turn.
