For pet insurance to take affect and before you can make a claim on the pet insurance and use it you need to wait for 14 days for most pet insurance policies before making a claim with the pet insurance company.
However if an accident occurs or another emergency with your pet then you may be able to use the pet insurance as soon as 48 hours after getting the pet insurance policy.
Basically it varies depending on the Pet insurance company and their policies but within 14 days you should be able to use the pet insurance.