As for hardware, there are 60 bay rackmount chassis out there that you can outfit with 60 20TB drives, which would give you just over 1.2PB. You would need a motherboard with enough PCIe lanes to use the needed number of HBA cards. If you went with HBA cards that can support 16 drives, you'd need 4 for 60 drives. I personally use the Pro WS WRX80E-SAGE SE WIFI, which might be overkill for your scenario, but the 7 16x lanes allows me 4x HBA cards + 1 GPU for Plex hardware transcoding/Steam streaming + 2 Hyper M.2 expansion cards for cache.

How small do you need to start?

And you need to define "FAST" with an actual number you need.

What’s the data you’re backing up and will it dedupe/compress well? How are you backing up software wise, veeam/comvault or will you be doing standard base line rsync etc? Does it need to be an enterprise system that you can fold into the existing backup strategy of the location or is it going to be separate and utilise secondhand equipment? Is a self hosted object storage system out of the equation or are you looking for best bang for buck for hdd purchase?

You can go with a single large capacity server, such as: https://www.45drives.com/products/storinator-xl60-configurations.php Or go with a cluster and a distributed file system. It's a lot less work/less complexity to go with a large single server. Performance wise, you either care most about the cost and use hard drives or you care most about speed and use some kind of solid state storage.

If I were you, I'd call a few storage vendors and see what they say. Compare feature vs cost and then decide if you want to roll your own.