We contracted a company to implement some of their products in our org, one of them is based on Einstein Analytics, so it requires Einstein Analytics to be enabled. If we don't have an add-on license from Salesforce regarding Einstein, can I still enable it? will I have to pay for it?
You can enable Einstein Analytics immediately in Salesforce org where you see this button. It won't cost you any additional money. It will be limited to a few thousand records which can be processed.
If you do not have license, button will not let you enable this feature. Org must have one of the license to use the feature. Check if you can see one or more of the following licenses in "Company Information" section in Salesforce org:-
More information on following link "Enable Analytics and Create Permission Sets"