Hi there,
Every person who is resident in Switzerland must be covered by compulsory Swiss health insurance, or an acceptable equivalent. You do have a 3-month window from the time you move to Switzerland within which you must take out a compulsory health insurance policy. However, the policy which you (eventually) take out covers you retroactively from the time you took up residence in Switzerland. You must pay premiums for the full period of coverage (from the time you became resident), and can claim benefits for medical expenses incurred during that time.
You can use the unbiased health insurance comparison on moneyland.ch to find the most affordable compulsory health insurance policy based on your place of residence, age, and preferred deductible and insurance model (unrestricted or managed care).
Best regards from Moneyguru