We present our search for strong lens, galaxy-scale systems in the first data release of the Dark Energy Survey (DES), based on a color-selected parent sample of 18 745 029 luminous red galaxies (LRGs). We used a convolutional neural network (CNN) to grade this LRG sample with values between 0 (non-lens) and 1 (lens). Our training set of mock lenses is data-driven, that is, it uses lensed sources taken from HST-COSMOS images and lensing galaxies from DES images of our LRG sample. A total of 76 582 cutouts were obtained with a score above 0.9, which were then visually inspected and classified into two catalogs. The first one contains 405 lens candidates, of which 90 present clear lensing features and counterparts, while the other 315 require more evidence, such as higher resolution imaging or spectra, to be conclusive. A total of 186 candidates are newly identified by our search, of which 16 are among the 90 most promising (best) candidates. The second catalog includes 539 ring galaxy candidates. This catalog will be a useful false positive sample for training future CNNs. For the 90 best lens candidates we carry out color-based deblending of the lens and source light without fitting any analytical profile to the data. This method is shown to be very efficient in the deblending, even for very compact objects and for objects with a complex morphology. Finally, from the 90 best lens candidates, we selected 52 systems with one single deflector to test an automated modeling pipeline that has the capacity to successfully model 79% of the sample within an acceptable computing runtime.