One way is using zero knowledge computational integrity proofs. They allow me to prove to you that I know of pre-image of some hash without revealing what it is.

Say the network has seen 1TB of data before with hash H. It can generate a random number as a challenge, and request a miner to prove they have access to the 1TB worth of pre-image at the same time it has access to the random challenge. The only way for a miner to compute such a proof is to have the 1TB of data stored somewhere.