What were your expectations for this role during the first month?

When bringing in a new Technical Lead the expectations I would have are, firstly, getting to know the team, processes and the technology stacks that are being used to deliver the current and future initiatives. Building relationships with your team members and fellow TLs really helps to get an understanding of your peers, their various levels and interests as well as an understanding of their motivations.

From a technical aspect, understanding the tech stack we use, the technical direction we want to be heading and a broad understanding of the product are vital in order to have the right conversations with your Product Manager going forward, so I would focus on obtaining that understanding rather than trying to comprehend every little feature that exists in the system (and there are a lot!).