How do I get a running start after landing?

Documentation about MC Connect and authentication between clouds: https://help.salesforce.com/articleView?id=mc_co_authentication.htm&type=0

Quote from above documentation: "Connected App Authentication is a secure authentication mechanism used by Marketing Cloud Connect. It removes the need to manage any Sales or Service Cloud user passwords in Marketing Cloud. It removes SOAP and REST API limits for Marketing Cloud Connect. Connected App Authentication does not lift BULK API limits. API calls made into the Marketing Cloud do not count against your daily limit."

If you are running API calls back and forth from Marketing Cloud to Sales Cloud outside either Apex or AMPscript, these are the limits you should expect: https://developer.salesforce.com/docs/atlas.en-us.salesforce_app_limits_cheatsheet.meta/salesforce_app_limits_cheatsheet/salesforce_app_limits_platform_api.htm

See the below documentation regarding temporarily/permanently increasing your organization's API limit: https://help.salesforce.com/articleView?id=000315571&language=en_US&type=1&mode=1

Hope this helps.