All we need to explain this is some illogical logic!
According to here Santa's average speed is 0.1x109Km/h and the speed of light is 1.1x109 Km/h which means he's bookin' at 10% the speed of light...
which is close enough to relativistic speeds for government work1
That means Santa will experience a doppler shift. Being at relativistic speeds, and knowing that e=mc2 then those same government agents can surmise that a part of Santa's mass is moving faster than the rest of Santa's mass. (This is all about Santa's mass, after all.)
We therefore conclude that Santa's mass is stretched by the speed he must travel. But his mass, itself, isn't changing, so the volume at any point along the length of the stretched mass is much smaller than his jolly girth would naturally be while standing still (or running alongside Olympic sprinter Usain Bolt, who cannot yet hit relativistic speeds... but he's working on it.).
By the application of what inevitablly will be some form of Fourier Transform (left as an exercise for the reader, along the lines of "how much of a student's mass can be kicked during a physics test?") what we'll discover is that the maximum diameter of an elongated Santa's mass including his sleigh is less than 10cm. We'll also discover that this increases Santa's efficiency as he will enter and exit dozens (if not hundreds) of houses simultaneously as an elongated mass entering chimney holes and delivering presents all at the same time.
Causality is known to be preserved by the empirical evidence of none of the houses exploding from the pressure change of air being forced through their chimneys at relativistic speeds in mere fractions of a second. But it does suggest that Santa's cookies are not pre-cooked before delivery.
1 You'd be surprised how many square pegs you can pound into round holes when you apply government standards.