There is no race to undertake gaining all modules (honestly) and satisfying all experience requirements (honestly, with NO embellishment). The minimum times set by EASA or any NAA to acheive all that is required for any AML issue is exactly that, MINIMUM.
Anyone wishing to be a safe licenced aircraft maintenance engineer should pour every effort into developing as a competent, confident technician in your field of expertise firstly, before ever gaining those full levels of responsibility.
Enjoy your career, join or make a good team, work hard & never stop learning.
BAe
Association of Licensed Aircraft Engineers (ALAE) - Welcome