What evidence is there for the fundamental assertion within Christianity that the Christian god exists in the first place?

None, as far as I'm aware! I'm not defending the religion.

What room is there for questioning that assertion?

In some factions, plenty. In others, not so much. I've met plenty of Christian folks that don't believe in intelligent design, and it's not like they're immediately ejected from the church - and this appears to even be true among Catholic leadership. It's a controversy.

And don’t give me that “intelligent design” bullshit

I think you have the wrong idea about me, which is understandable, given how annoying I'm being.