Not knowing what costs you have already occurred, but waiting to take your insurance out till just before you depart, means that you are foregoing one of TI's significant benefits - which is if you have to cancel your trip for a reason covered by TI.
ie in My case I had a major European trip all arranged two years back, and my wife had a major accident which prevented her from flying for 6 months. If I had waited till near departure to activate my TI, I would have been out of pocket for quite a substantive sum.
IMO as soon as one starts paying any significant amounts, one should make sure that you have activated travel insurance. This is why policies that you pay for ask for your departure date.
In my case as I redeem virtually all international flights a year out which are cancel-able for only a minor fee, I tend to activate my insurance as soon as I start committing to other expenses such as trains, local flights, tours, accommodation etc.
sometimes this is paid insurance, and sometimes it is credit card insurance.