Where do people who give away hundreds of games at a time get the games they give away?

A secret... you want to know?
come a little closer...

Most likely either accumulated through bundle purchases or they do some sort of work where they receive promotional keys from developers/publishers.

cg buys them for me, so i can get more SG levels.
joking aside, we buy them. mostly at discounts, a lot from bundles...

Sales, bundles ext.

IndieGala 40-packs and OtakuMaker 10-packs are viable, but in most cases, 10+ packs mean they got (sometimes extorted) them from the dev/publisher for promotional reasons.

I emailed some devs a couple years ago cause I needed a buncha copies of a game for a giveaway and I really didn't feel like spending a few hours doing it manually through Steam and they got me set up with keys.

it's called farming developer keys. the new way of leveling up for no cost.