Sheldon is watching the premiere episode of Star Trek: Deep Space Nine (1993): Emissary (1993), which sets this episode's date as the week of January 3, 1993.
Sheldon's reaction to his mom making pancakes on Sunday is very reminiscent of The Big Bang Theory (2007): The Gothowitz Deviation (2009), when Penny offers to make him French Toast and he tells her no, because it's his morning to eat oatmeal.
Amber calls Georgie a "soccer mom". Based on the premier date of Deep Space Nine, this episode takes place in 1993, but the term "soccer mom" wasn't used until 1995.