Well the best time to buy health insurance is at the Earliest because here is my take on the same:
1. When you take health insurance as early as possible the premium will be very less so one thing is earlier it is, better it is on the pockets
2. One more thing is you're less likely to have pre-existing conditions that could be excluded from coverage.
3. And we cannot go with the assumptions that we will be fit and fine for a certain amount of time, so its better to take the plan early
And added benefit is, if you have selected old tax regime then you can also claim deductions under Section 80D