Can an actual expert in EC confirm or deny this simple statement?

Considering the secp256k1 curve, and the existence of symmetry and lambda endomorphism, there can not exist any algorithm that solves the ECDLP over an interval in less than sqrt(b) group operations (with no precomputation required).

From what I "know" the complexity cofactors are something like: BSGS: 1, Rho: 1.25, normal kangaroo: 2, four-kangaroo: 1.71, Gaudry-Schost: 1.36

If the answer is no, what can happen if it is proven otherwise? If the answer is yes, is there a known lower bound? And maybe a research paper?