The Xbox Series X was a tad easier to find when the PS5 was in short supply. And by that I mean it was at least easier to get without compulsively monitoring stock trackers. However, that doesn't mean it'll be any cheaper during Prime Big Deal Days.
Like Sony's PS5, the Xbox Series X might not be discounted on its own for Amazon's October Prime Day event, but moderate bundle discounts are more likely to be available. You may have to wait until the holiday shopping season to officially kick off before you see a significant discount.
Right now you can find the console for $490 at Amazon -- a modest $10 discount. However, if you really want an X, but can't afford to pay the $500 upfront and you have reasonable credit, you have the option of getting it through Xbox All Access for $35 per month (24 months). The catch is it includes two years of Xbox Game Pass Ultimate, making the total well over what you'd pay for the console alone, which includes only three months of XGPU. But XGPU really is worth subscribing to, and while you don't save a lot through All Access, you don't pay more than you would otherwise.