The prevalent 0.33 NA unobstructed extreme ultraviolet lithography (EUVL) six-mirror objective system is characterized by a large average incidence angle at M5, which adversely affects imaging performance and energy transmission following coating. In order to improve the system performance of coated EUVL objectives, this paper presents an innovative 0.36 NA EUVL objective system, to our knowledge, designed to mitigate these issues by reducing the average incidence angle. Meanwhile, the genetic adaptive particle swarm hybrid effective set algorithm (GA-APSO-Aset), which does not need to provide a starting point, is proposed to search the initial structure of the new system, and further optimized. It achieves comprehensive wavefront aberration across the full field-of-view (FOV), exceeding the benchmark of 1/60λ (λ=13.5nm). In comparison to a conventional 0.33 NA unobstructed EUVL system, the new system exhibits an enhanced average light transmission of over 26% post-coating, providing a strategic approach for the integrated design of EUVL coatings and objective systems.