A Swiss phone number in one afternoon
You will want a Swiss number for two-factor codes, delivery slips, and being treated as a resident.
Prepaid SIMs at Migros, Coop, or Salt shops cost around CHF 10 and work the same afternoon. Good for the first month.
For a contract, Salt is usually cheapest, Swisscom has the best coverage in the mountains, and Sunrise sits in the middle. Wingo, Yallo, and M-Budget are the low-cost virtual carriers on those same networks.
You can keep your foreign number active on eSIM for another few weeks while your family adjusts. No rush to cancel abroad.