Joining an existing team can be quite challenging.

Work is already in progress, you lack significant (sometimes basic) knowledge, have no pre-existing relationships and are expected to make an impact in a relatively short period of time.

A useful strategy for ramping up quickly as an Engineering Manager is running Boz Algorithm (Thanks Gilad!).

On your second day at work, meet with a team member and:

1. Ask him to tell you everything he thinks you should know. Listen and take notes.
2. Ask about the biggest challenges the team has right now.
3. Ask who else you should talk to: write down all the names.

Recursively run the algorithm on anyone listed at (3).

From (1), you can quickly identify issues that bother team right now and require action. It will also get you familiar with current terminology team uses ("That XY Pipeline...."). This can be tricky, as not everyone will answer right away, so try rephrasing your question ("Is there anything technical you think I should know?", "Product/People/Process?")

From (2), you can identify low-effort items that are important to the team. This will allow you to make a quick impact.("Kanban board is a mess", "So many meetings....", "Daily is so long...", etc).

From (3), you can quickly create a map of influence within the organization. The frequency and context in which names appear will let you know on who to focus more at the very beginning.