Preterm babies in the Neonatal Intensive Care Unit (NICU) have to undergo continuous monitoring of their cardiac health. Conventional monitoring approaches are contact-based, making the neonates prone to various nosocomial infections. Video-based monitoring approaches have opened up potential avenues for contactless measurement. This work presents a pipeline for remote estimation of cardiopulmonary signals from videos in NICU setup. We have proposed an end-to-end deep learning (DL) model that integrates a non-learning based approach to generate surrogate ground truth (SGT) labels for supervision, thus refraining from direct dependency on true ground truth labels. We have performed an extended qualitative and quantitative analysis to examine the efficacy of our proposed DL-based pipeline and achieved an overall average mean absolute error of 4.6 beats per minute (bpm) and root mean square error of 6.2 bpm in the estimated heart rate.