You can typically use your health plan after the insurance company approves your application and issues you a policy number, starting from the coverage start date. Many doctors' offices will accept your policy number for billing purposes before you receive your card.
 
If you don't have a policy number yet but your coverage is active, you may need to pay the bill at the time of service, then file a claim with your insurance company for reimbursement after you receive your policy number or insurance card.