What do you aim to achieve in first 2-4 weeks of a new job?

Get myself feel onboarded which can be different than whatever onboarding was planned for me. For me that's being able to ship a change to the core system I'll be working on. That paves a green path in process. Be aware of and have access to the logs, stats/SLIs. Choose my editor/IDE and be able to run the (sub)system and tests locally.

The other thing I usually want and make is a complete ERD or complete ERD of the teams specific area and connections to other areas. Knowing the logically-unique keys for every table and effective FK relationships and cardinalities can tell you a whole lot very quickly and accurately.

Learn terminology and conceptualization (both technical and product-customer focused ones) to put everything above and more into context.

Get assigned to an ongoing or new project (or mini-project), fixing bugs is a fantastic way. Allows for deep-dives that cover depth through layers of the system and learn to navigate the codebase and logs, stats, what questions to ask.

Start understanding performance or scaling issues, either already identified or be able to discover them by accessing stats or error/slow query logs, etc.

Understanding the codebase is low on my list of priorities and approached tactically. For a specific given task, learn as much as I need to know and not too much more. Slowly and organically learn the typically undocumented architecture details, again on a need-to-know basis. All these things become higher priority later.

I think the most important thing is to find out what your superior expects you to achieve in the first 1, 3, 6 months, how you can get there and who can help you getting there. Too many people live in fear, because they don't know if they do well. Just ask what people expect!

The next important goal might be getting to know the people, their views. Ask a lot of questions. Don't try to seem smart - ask all the dumb question at the beginning. It gets harder to ask them the longer you are on the job.

Probably figure out where everything is and what I don't have access to. Onboarding is a pain in the ass. I've always regretted trying to rush it and jumping straight to work. Before you start chopping, make sure they gave you a sharp axe.

I think this is the wrong question to ask, potentially. The right question to ask is, "If I've done this job well, what will I have solved/accomplished in the first year?"

Salaries, benefits, titles, etc aren't invested in unless the need is real, and real needs take time to solve. The first month is familiarizing yourself with the problem you need to solve, and the culture of the organization.

I would want the company to provide detailed and accurate information on all their systems, their structure and architecture. I would also want to be set up with all the tools I need.