Unfortunately you will not be able to access the Data API on the Start Plan. If you are looking to set up integrations with CRM providers, you will need to upgrade to get the Grow Plan to gain access to the Data API's.
Here are some instructions on how to upgrade your account to the Grow Plan: https://justgiving-charity-support.zendesk.com/hc/en-us/articles/235881588-Upgrading-from-the-Start-Plan-to-the-Grow-Plan-UK-ONLY