While timings can differ, generally US retailers launch Xbox Series X restocks in the late morning / early afternoon ET. Best Buy typically drops at around 12pm ET / 9am PT, with GameStop offering earlier drops from 10.30am ET / 7.30am PT onwards. Walmart has stuck to a fairly rigid 3pm ET / 12pm PT launch schedule over the last few months, however. That means we'd recommend keeping your hunt up between the hours of 10am ET / 7am PT and 4pm ET / 1pm PT.
Over in the UK, however, Xbox Series X restocks typically land in the morning. Game is known to drop its stock before 9am, but sites like Ebuyer, AO, Argos, and The Game Collection aren't too far behind, all dropping stock before midday in general.