Unless it is graded death benefit which means the coverage is limited for the first 2-3 years you own the policy, then after that timeframe, you have full coverage.
However, if you have been accepted for life insurance, signed the forms and paid your first month's premium, you should be insured.
You can want to review your life insurance policy, call your life insurance agent or carrier, and ask this question to verify whether your life insurance coverage is "In Force".
In addition, there are life insurance plans you can apply for online and if approved you may start your life insurance coverage the same day.