"I don't get why people think the big bang and God cannot both exist and be true at the same time. Please share and help me understand."

Big bang theory suggests an ever expanding universe and requires a relativistic understanding of cosmos and its natural consequence - the heliocentric model.
The bible suggests a closed system with God overseeing and controling everything. How can you explain something like Isaiah 38:7,8 "This will be a sign to you from the LORD that He will do what He has promised: I will make the sun’s shadow that falls on the stairway of Ahaz go ten steps backward.” using science? I think Christianity is completely incompatible with the current form of science.

"Why give humans the ability to ask "what if" and natural desire to learn and explore but expect them to believe the Earth is only 5,000 years old. It simply is not."

Such dogmatic certainty you have. Have you sacrificed sweet smelling burnt offerings to Einstein lately?