Make Real Connections at a New Job

The first week everyone was friendly and then the second week everyone was busy and you are not sure where you stand. This covers what to do with those first two weeks before the window closes: how to find the people who know what is actually going on, how to build a real relationship with your manager before you need one, and the one thing that frequently undermines otherwise sensible new starters.

I have just started a new job and want to build genuine working relationships with my colleagues, not just surface-level familiarity. Help me with:
1. The first two weeks: what to prioritise in terms of relationships before the work takes over
2. How to make a good impression in group settings without dominating or disappearing
3. How to build a one-to-one relationship with my manager in the first month
4. How to find the informal knowledge networks: who actually knows what, and how to access them without looking lost
5. One thing to avoid doing in the first month that frequently sets people back

This is an office or hybrid environment. Keep the advice practical and not advice-column generic.