Time-delay cosmography can be used to infer the Hubble parameter H-0 by measuring the relative time delays between multiple images of gravitationally lensed quasars. A few of such systems have already been used to measure H-0: Their time delays were determined from the light curves of the multiple images obtained by regular, years long, monitoring campaigns. Such campaigns can hardly be performed by any telescope: many facilities are often oversubscribed with a large amount of observational requests to fulfill. While the ideal systems for time-delay measurements are lensed quasars whose images are well resolved by the instruments, several lensed quasars have a small angular separation between the multiple images, and would appear as a single, unresolved, image to a large number of telescopes featuring poor angular resolutions or located in not privileged geographical sites. Methods allowing to infer the time delay also from unresolved light curves would boost the potential of such telescopes and greatly increase the available statistics for H-0 measurements. This work presents a study of unresolved lensed quasar systems to estimate the time delay using a deep learning-based approach that exploits the capabilities of one-dimensional convolutional neural networks. Experiments on state-of-the-art simulations of unresolved light curves show the potential of the proposed method and pave the way for future applications in time-delay cosmography.