This clearly indicates either the connections, cables, or the solenoid/starter is bad. Unless,,, you have a bad ground.
I suggest that you spend a few minutes cleaning the ground contacts with emery cloth to make sure they are all clean & doing their job, expecially the large one going to the engine/trans as it is the one needed for cranking the engine, the small grounds provide the finishing circuit for the electrical system beyond the starting system.
Make sure your battery terminals are exceptionally clean, tight fitting on clean posts & tightened to where they are snug, then coat with grease to seal & protect.
Recharge the battery if it is not above 12 Volts. A new battery doesn't reach peak voltage until charged. Most parts stores sell the
batteries with the charge that they built by adding the electrolite & it usually works fine, but cold weather dictates that they should be charged before being installed to prevent excessive wear on the alternator which has to work extra hard to charge a weak battery & keep the car going with all of the accesories working.
You should also check the starter/solenoid main connections for corrosion, and while you have any
cable in your hand, bend it & listen to see if you hear the corrosion inside the cable making noise. If so, replace the cable.
If you've don all of this and it won't crank, take the starter off & go get it bench tested, it or the solenoid should be the problem at this point.
t's a lot of info, but there are many considerations to the entire starting system.
Good luck