We construct a novel Multi-Input Multi-Output Autoencoder-decoder (MIMO-AE) to capture the non-linear relationship of Southern California precipitation (SC-PRECIP) and tropical Pacific Ocean sea surface temperature (TP-SST). The MIMO-AE is trained on both monthly TP-SST and SC-PRECIP anomalies simultaneously. The co-variability of the two fields in the MIMO-AE shared nonlinear latent space can be condensed into an index, termed the MIMO-AE index. We use a transfer learning approach to train a MIMO-AE on the combined dataset of 100 years of output from a historical simulation with the Energy Exascale Earth Systems Model version 1 (E3SMv1) and a segment of observational data. We further use Long Short-Term Memory (LSTM) networks to assess sub-seasonal predictability of SC-PRECIP using the MIMO-AE index. We find that the MIMO-AE index provides enhanced predictability of SC-PRECIP for a lead-time of up-to four months as compared to Ni{\~n}o 3.4 index and the El Ni{\~n}o Southern Oscillation Longitudinal Index.