Comet Interceptor (Comet-I) was selected in June 2019 as the first ESA F-Class mission and aims to explore a pristine comet, which will visit the inner Solar System for the first time. Comet-I will hitch a ride to a Sun-Earth L2 quasi-halo orbit, as a co-passenger in ESA's M4 ARIEL's launch. At the time of writing, this is scheduled for 2029. It will then remain there awaiting the right departure conditions to leave definitively and intercept a newly discovered comet. Comet-I will be the first mission to be designed and launched without an already identified target. Given the latter, the Comet-I Target Identification Working Group is tasked with the continuous follow-up of newly discovered comets, to analyse their characteristics as virtual targets for Comet-I. The goal of the paper is to inform the decision-making process that will eventually be necessary to commit Comet-I spacecraft to its final target.Within this context, this paper presents a trajectory optimization process based on Primer Vector theory that considers intercept trajectories with multiple revolutions and multiple deep space manoeuvres (DSM). The process is applied to 21 long period comets, which were discovered since July 1, 2020 and whose characteristics are of interest for the Comet-I mission. In fact, one of the latest of these recently discovered comets, C/2023H2, is the most accessible virtual target discovered at the time of writing, with delta-V intercept costs well within Comet-I capabilities. A complete launch window analysis is thus presented for C/2023H2, which accounts not only for the most optimal delta-V intercept transfer, but also considers all launch options that satisfy all Comet-I's current boundary conditions and flyby constraints. A systematic launch window analysis is made possible by a grid search approach on which departure and fly-by dates are fixed and the remaining design variables, including the times for manoeuvres and their Δv impulse vector, are optimized via Primer Vector theory. This allows to understand the latest possible departure date, but also the sensitivity to departure and arrival dates of key encounter characteristics such as relative fly-by speed, the solar aspect angle and the Earth distance.