No. It will take a decade to build enough Starship to have 1000 in operation. At that point, each will launch 3 times a day, for a total of about 1000 a year. One million per year in total. Not tomorrow, but starting about a decade from now.
Getting a little pedantic, but presumably some of those will be heading to or from Mars at any given time.
Anyway, it’s a long ways out and has nothing to do with the immediate Starship launch plans.