To send a welcome email with a coupon to first-time customers immediately after they sign up for a newsletter, the associate should use Automation Studio within Salesforce Marketing Cloud. Automation Studio offers a powerful suite of tools for automating marketing and operational tasks, including triggering emails based on specific events or actions, such as a new newsletter sign-up.

By setting up a trigger-based automation in Automation Studio, the marketing team can ensure that as soon as a new sign-up is recorded, the welcome email is automatically dispatched. This immediate and personalized response can enhance the customer experience and foster a positive relationship from the outset.

References: Salesforce Marketing Cloud's Automation Studio documentation provides comprehensive guidance on creating and managing automations, including trigger-based email sends, to optimize marketing processes and enhance customer engagement.