By default, when a case is created, Salesforce will not automatically select the Entitlement for you. To do this, you will have to customise it yourself:
1) Create a default checkbox at the Entitlement object. Also you will need to make this checkbox unique across the same Account. For example, if CompanyA has 3 different types of entitlements, there should be only one default entitlement.
2) Create a trigger at the Case level to listen to Create/Update event. When a case is created, if the Case.Account is provided, automatically assign the default entitlement to the case.
Note: In most situation, the Account record should not change. If this situation applies in your scenario, you may need to create the trigger to handle this event. If a different entitlement is selected, please ensure that it does not affect the existing milestone history.