Who says BTC keys are 10^77? Secp256k1 elliptic curve group order is :
If you add this to N
You will reach 2^256, and nobody can count the atoms in the universe, even that estimation is around 863 times greater that 2^256, but that's not the point, also pandora box only brings misery and despair if you open it, not luck.
The only physically possible way to find a private key( other than taking it by force ), is through working on public keys, and guess what? Public key cryptography is counting on the difficulty of doing that, it says "here I'm open in the public, throw your best at me" and it is safe because throwing the best is proven to be difficult to do, SO far.