With some providers, you’ll have the option for instant credit card approval and use. For example, some American Express and Bank of America cards come with card numbers you can use instantly upon approval. You can use these numbers to add the cards to your existing wallets within the same bank or use them in stores where a physical card is not explicitly required.
If you have your bank’s local branch nearby, visit it and check whether you can get temporary cards which you can use while your cards arrive in the mail.