Nathan, an adult who cosplays as Jean Luc Picard, is played by Steve Burns, who wrote the theme song for Young Sheldon. He was also the original host for the Nickelodeon show Blue's Clues (1996).
The comic convention takes place on March 6th, 7th, 8th. If this were held over a 3 day weekend, that would set this season in 1992.
On the bus to the convention someone says, "If Lost in Space (1965) is so great, how come they haven't remade it?". After the time this story is set, it was made into a movie (Lost in Space (1998)) and then a new series (Lost in Space (2018)).
The bus station that Sheldon comes in and out of is actually the remodeled exterior of Luke's diner from Gilmore Girls (2000). The "Young Sheldon" series often uses other exteriors from the Warner Bro's Midwest Street backlot.
Nathan calls Lost in Lost in Space (1965) kids' show. Nathan is played by Steve Burns who formerly hosted Blue's Clues (1996), a kids' show, from 1996 to 2002.