Consider the facts:

-TLJ establishes that the Force can arise in anyone, and GL has claimed that anyone can learn to use it.
-Han has spent thirty years around the most powerful Force users in the galaxy.
-He is a believer in the Force and has been for decades by the time of TFA.
-He has always had an abundance of luck, trusts his feelings over his rational mind, and is a quick draw with a blaster even in his early days.
-In ROTJ he shoots the Sarlacc without the use of his eyes (‘Trust me’), and in TFA he headshots a Stormtrooper without looking at him at all.
-He is able to exit Hyperspace between the Starkiller’s shields and the planet’s crust, a feat lifted from an early script of TPM where only Anakin’s Force ability was able to manage such a thing.