If all parties can trust a common randomness beacon (like the NIST Randomness Beacon), this can be achieved by including a recent block from the beacon into the file along with its timestamp. The recipients then, in addition to verifying the signature, must also verify that the beacon data is authentic and as recent as they require.
Other public random values might also do the trick, for example, the winning numbers of a well-publicized lottery. But care needs to be exercised however that the items chosen have sufficient entropy. For example, if you just pick the closing value of the Dow Jones Industrial Average, that's been a 6- or 7-digit value for decades, so an attacker could just force you to precompute signatures for all likely future values of the index. The closing values of a list of stocks that all participants agree on beforehand might do the trick, though I'd want to do some calculations first to convince myself that the list has sufficient entropy.