The Gran Telescopio de Canarias Adaptive Optic System (GTCAO) is built to provide nearly diffraction-limited images to GTC. GRANCAIN (GRAN CAmara INfrarroja) is the first light cryogenic imaging instrument in J, H, and K infrared bands, which will be integrated into the Nasmyth focus of GTCAO. The instrument is designed to image the NIR (NearInfrared) diffraction limit for a field of view of 22x22 arcsec operating up to conditions of 1.5 arcsec and zenithal distances up to 60 deg. The instrument has a telecentric optical design based on a collimator camera with a 2:1 magnification, with a cold stop, and the filters between with an infrared detector everything inside the cryostat for operating at 50 K. This article presents a comprehensive overview of the end-to-end optical design of GRANCAIN. It explores the selection criteria for diverse commercial elements, conducts thermal analysis utilizing Ansys Zemax OpticStudio, and delineates the acceptance tests performed at the IAC. The article also encompasses tolerance analysis using Ansys Zemax OpticStudio and establishing the error budget. Furthermore, the text provides a detailed account of the alignment process, achieved through the mechanical positioning of each optical element with a laser tracker and the confirmation of positions under cryogenic conditions is conducted using an alignment telescope. Lastly, the article discusses the optical acceptance plans for the instrument before its integration into GTCAO.