How can I build a bigger presence within the team and make progress towards senior?

Some fundamentals I believe apply to any promo:

• Observe SE3s on your team and figure out how they behave and the impact they deliver.
• Work with your manager to create an expectations plan to progress towards SE3, which is ideally as close to a checklist as possible.

At your stage in career, I wouldn't expect the ability to draw large, clear lines between your work and business impact: That's more of an expectation at senior from my experience. I think in your situation, at a high level, focus on knocking it out of the park with the projects you are given and don't worry too much about the business impact of each project.

In terms of what an engineer on the earlier side of mid-level can do:

• Set the example: The foundation for any senior engineer is the ability to produce extremely high-quality code with solid velocity and great technical depth. I think this is the most straightforward way to level up. An insight here is that writing the code is just 1 way to influence the production of high-quality code: The other angle is reviewing other people's code and holding the bar. A big mindset shift growing to the higher-end of mid-level and then to senior is that you should wield huge influence in code review, leveling up the team's code.
• Speak up in meetings: This is the most literal when it comes to visibility. Progressing to upper mid-level and beyond means that you should have strong opinions on anything technical and be able to eloquently share them. Can you say something meaningful in every team meeting?

Related resources:

• Building Reputation As An Earlier-In-Career SWE
• Advice On Being More Active In Meetings
• Full Session On Effective Code Review