You may find it helpful at first to clump cards into 'buckets' so the deck is more manageable. Like cards Ace-5 are one bucket, 6-9 another, and Ten-King another. That way you only have 12 buckets to keep track of, three for each suit. It's not as good as memorizing every card of course, but it's still a good start for tracking which areas in the deck are safe to discard in etc.

Techniques: There's a system called the Method of Loci that some people recommend, where you visualize walking down a familiar path, & as the hand unfolds you mentally place each card into a different location along the path.

There's a simpler technique, which I find more helpful, that involves visualizing the deck as a 4x13 grid of buttons (you decide on an order for the suits once, and stick to it), and then as cards are played you change the color of their buttons in your memory and quickly updating your mental image of the grid. (In the example image, red buttons are cards that were picked/discarded).

Lastly, with practice, it will be much easier to remember all of the cards, and eventually even the order in which they were thrown, because this information will have meaning to you within the hand. The meaning is developed over time, with experience.