That’s a reasonable concern! You can just place the cards at the bottom of your deck rather than using a discard pile.
(While you could certainly shuffle the deck between every draw, it’s a variant rule for a reason - I find it changes the feel of the game a slight but significant amount. It’s great if that extra layer of uncertainty is what you want to opt in for, but placing the cards at the bottom of the deck is a better way to get the standard experience if that’s what you want!)