Did Christianity invent hospitals and charity?

Yes, in an important sense — though the claim has to be made carefully. Christians did not invent all kindness; individual pagans loved their children and could be moved to pity, and Stoic writers reasoned about a shared humanity. The narrower claim survives all of that: no ancient Mediterranean civilisation outside Israel rested a law, a movement, or an institution on the conviction that the weak, as the weak, have first claim on the strong.

That reflex came from two Jewish-rooted convictions welded together — that every person bears God's image, so worth cannot be forfeited by weakness, and that God himself stooped to the lowest (“whatever you did for the least of these, you did for me”). Out of it came institutions, including the charitably endowed hospital for the sick poor — not that Christians invented all care, but that this kind of institution had no clear precedent.

Isn't this just evolved empathy? Kin loyalty and reciprocal help are things nature can produce, because they pay. But caring for the useless stranger, or the enemy who can never repay you, goes beyond anything reciprocity explains — Nietzsche saw that it runs against nature, and hated it for exactly that reason.

None of this proves Christianity is true — a belief can remake the world and still be false. The case rests on the resurrection, argued elsewhere; this only shows where a particular moral reflex was learned.