Hmmm A challenge to prove Santa Claus is real. Suesa's Science Challenge #3 A Very Science Challenge and my entry.
I'll start off with how Santa could know if we were bad or good. Our electronic age has made Santa's job much easier on the old guy. Those chips in the cell phones, televisions, I pods even the Alexa home base has made Santa aware of everything we are doing. The cell phones in mommy & daddy's pockets pick up all the conversations so Santa can know how good you've been this year. He's been keeping notes with his Apple phone. Data is downloaded from multiple sources including the cameras throughout the world.
Source: Computerworld.com
Santa has his data base in a base under Antarctica. Santa's elves have been building it since the mid 1900's. The base houses his "super sleigh" which was built by Lockheed Martin. The super quiet sleigh has sound barrier breaking speed to travel the world in the few hours Santa has to delivery those gifts. A laser beam attachment allows Santa to precision deliver presents without a sound. The gifts are only holograms, he doesn't actually bring them. Simply linking his Apple phone with the workshop with the correlating child's address, these high tech lasers create everything from the circuit boards for the electronic gifts to the outer shapes of toys & gifts, all in a matter of seconds.
Source: Hexapolis.com
As the beam targets through a window, usually where the Christmas tree is, the beam materializes the gifts Santa has on his list. The beauty of the laser beam is multiple houses can be targeted in the span of just a few seconds. This laser technology was passed onto Santa from Finland where they have created 3-D models from a laser. This has made gift delivery easier than filling the sleigh several times a night.
Source: atlanteanconspiracy.com
The beauty of time changes throughout the world makes Santa's job very easy for a one night delivery. And because only a select few celebrate Christmas with letters to Santa, he doesn't have to deliver to everyone. As far as Rudolph the red nosed reindeer, he's really just a deer at the base. Reindeer wouldn't be able to handle the pressure and speed by the super sleigh. But he is Santa's favorite and he does have a red nose.
Source: commons.wikimedia.org
Scientific backup & further reading:
An Underground Base In Antarctica:
http://www.subterraneanbases.com/an-underground-base-in-the-antarctica/
Missions Impossible: The Skunk Works Story:
https://www.lockheedmartin.com/us/100years/stories/skunk-works.html
Researchers Fabricate 3-D Silicon Structures With A Focused Infrared Laser:
https://phys.org/news/2017-10-fabricate-d-silicon-focused-infrared.html
The Scientific Reason Why Reindeer Have Red Noses:
https://www.smithsonianmag.com/science-nature/the-scientific-reason-why-reindeer-have-red-noses-166263479/
See 
https://steemit.com/science/@suesa/suesa-s-science-challenge-3-a-very-science-christmas