Well all the txns are distilled down to a single merkle root hash which only has 256 bits.  Originally I was thinking an infinite number of merkle trees but that doesn't matter because there is still a finite number of merkle root hashes.  Still even with nothing else 256 bit for merkle root hash + 32 bit nonce + 32 bit timestamp = 320 bits.  Still infinite or finite as you pointed out unless you some subset of the values are more likely to produce a solution it doesn't matter where you start.