From log-normal simulated LSST Y10-like convergence maps, we constrain wCDM parameters using two approaches: (1) the explicit full-field inference (black), obtained by sampling 160 000 posterior samples through an HMC scheme; and (2) the implicit full-field inference contours (blue), obtained by compressing the convergence maps into sufficient statistics using variation mutual information maximization (VMIM) and performing inference using NLE with 1000 simulations. We show three things: (1) implicit and explicit full-field inferences yield consistent constraints; (2) our implicit inference, when combined with an optimal compression procedure, allows full-field inference; (3) the C2ST metric indicates convergence when it is equal to 0.5 (see Sect. 4). However, when comparing explicit and implicit inference (which should theoretically yield the same posterior), we never reach this value, but rather we obtain 0.6. We justify that this value is acceptable and use it as a threshold for all benchmarked methods in this paper by showing that the marginals of the two approaches match, even though their C2ST is 0.6.