GW170817 has led to the first example of multi-messenger astronomy with observations from gravitational wave interferometers and electromagnetic telescopes combined to characterise the source. However, detections of the early inspiral phase by the gravitational wave detectors would allow the observation of the earlier stages of the merger in the electromagnetic band, improving multi-messenger astronomy and giving access to new information. In this paper, we introduce a new machine-learning-based approach to produce early-warning alerts for an inspiraling binary neutron star system, based only on the early inspiral part of the signal. We give a proof of concept to show the possibility to use a combination of small convolutional neural networks trained on the whitened detector strain in the time domain to detect and classify early inspirals. Each of those is targeting a specific range of chirp masses dividing the binary neutron star category into three sub-classes: light, intermediate and heavy. In this work, we focus on one LIGO detector at design sensitivity and generate noise from the design power spectral density. We show that within this setup it is possible to produce an early alert up to 100 seconds before the merger for the best-case scenario. We also present some future upgrades that will enhance the detection capabilities of our convolutional neural networks. Finally, we also show that the current number of detections for a realistic binary neutron star population is comparable to that of matched filtering and that there is a high probability to detect GW170817- and GW190425-like events at design sensitivity.