Should I log flying lessons from the start? I've recently started taking flying lessons and was wondering if I should begin logging my flying hours immediately?

I'm aware there are minimum hours for each license certification, so I'm assuming I should be noting down my flight time right from the start but my instructor hasn't really said anything about it yet.
Yes, you should be logging from the start. Now for the first few lessons, it'd be ok to not have your own logbook yet, but you should get one. Hopefully your instructor has kept his up to date, and can build your logbook in terms of flight times since you started.