You are confusing the biased-nonce attack with brute force. The lattice attacks require a bias on the generation of the nonce to recover the key.
Brute-forcing the nonce, on the other hand, is not possible for a classical attacker if you use a 256-bit curve since $k$ is chosen from $[1,n-1]$ uniform randomly where $n$ is the order of the base point $G$.