I go in the Spirit of your question
Mind you this very rough Calculations - with very little info on the population denity or the total number of the people on Santa Route but Here I go -
the Earth is about 25,000 miles long, going around the world going from the North pole to the south pole and back to the North pole again allowing the Earth to rotate under him which spins at 1047.1976 miles per hour (Longitude ) since he turn round at the South pole because the other half of the Earth is in day light so he doesn't travel on the daylight longitude on that side of the Earth and it cut his travel time in half , and assume there are 6,6000 people along that Longtitude ( for a 60 ft x 50ft plot of land for a house gave or take a couple of thousand miles for the ocean and the number of people ) travel along that longtitude ( he as to see about 2,083 people per hour or 34.71666666 people per second ) to do that, he must reach those houses in 1. 0 microseconds to get to ,in the house, deliever the presents and leave and still make in time to reach the other houses ( of course if he Has the Elves help him he can cut the time in 1/(n+1) microseconds . Man, no wonder he so fat . and has eat a lot of cookies and christmas candies, he needs it, to keep his engery up. moving that fast. Any way my best estament would be round 1 /10 the speed of light to do it . but it could be done. But I think his job get harder each year with the number of kids being born in the world. fortunely, some of those kids stop believing in him So he doesn't have to deliver toys to them. Maybe you send this one to PI R Squared and see what he says about?