We had this discussion at work the other day among a few of us who started work remotely during the pandemic. We had actually had not been to the office and not met any of our co-workers face-to-face.
Someone posted the question of what was the most instrumental thing to effectively ramp up and feel like we had arrived at the company.
I had to think about this for a while but then it dawned on me because I had done it wrong before.

I have been in my current role for 3 months and I had ambitious plans from the start. Already during the interview process, I was showing off with a "Month 1, Quarter 1, Year 1" plan. I felt so sure about my "ticking the boxes" approach, but now 3 months in, I am not so sure anymore.

What is really most important? Is it:

Well, probably a little of everything but I realised that many of these can be learned and discovered over time. In fact many must be learned over time since there are too many "unknown Unknows" at the beginning to even know what questions to ask. So I relaxed a little and gave myself permission to run into a few walls, then ask questions and then discover how everything plays together. 

Instead I spent most of my time on actually building relationships and here are a few insights that have worked for me:

Plan it like a treasure hunt
"Failing to plan is planning to fail" said Ben Franklin and he was probably right. For myself that comes in form of a treasure hunt list as a spreadsheet. In the first column are just a list of names I somehow came across.
This could be people in my immediate team, people in the wider team, people I noticed in meetings or emails or recommendations from other people I met before.
Then in the other columns I would give myself things to find out about those folks. e.g. time at the company, current role, how does their role interact with mine/my team, where are they from, what's their favourite song at the moment, what hobby do they enjoy most etc.
I am purposely mixing work and life related topics because I actually want to get to know them a little closer as a whole person, not just their work side.
Sometimes I even assume something about the person to hear what they think and provoke a strong reaction. e.g. "I've noticed that you worked in 4 startups in the last 5 years, you must be bored to death right now!?"
You'd be surprised what types of insights you can get about the person, about startups, about the world even!

Be genuinely curious
Be honest with yourself. When you meet someone for the first time, or the second or maybe you've known them for long, how curious are you really about them? I have done this plenty myself, I listen to someone speak in order to just reply with my own knowledge and input and awesome story. That's not right.
The guiding principle here is "listen to understand instead of listen to reply", this will do something magical with the other person, they will feel that you are actually truly interested in them and therefore likely be way more open and honest with you. If it's meant to be, then you are on the path to building a lasting and deep relationship.
What has helped me personally as well is to really switch off distractions, shut down ping, email, flip over the phone and really tune into the person. This will allow you to pick up on emotional cues too, is the person smiling slightly, during which topics do their eyes really start to glow, what part makes them look a little overwhelmed or maybe even sad.
Going deep in that way will also allow you to discover possible ways to help the other person. Maybe you have expertise in a field they struggle with, maybe you know someone who can support them in some endeavour, maybe they know something that may help someone else you know and you can be the connector... 

Allow yourself to meet others
This sounds a little weird, but I think many of us carry some level of impostor syndrome which makes us avoid reaching out to certain people due to thoughts like "they are too important to talk to me" or "their calendar is already so busy" or "what can they possibly get out of a conversation with me".
My recommendation here is to drop this line of thinking immediately. It does not serve you well and it never will.
Every person on this planet has something to give. Yes you too. It might not be obvious before chatting with someone else, but trust me on this.
Does this mean that you will be friends for life with every new person you meet? Of course not. Some people you may only meet once and that is perfectly fine. Once in a while though, you will strike a chord with someone and plant the seed of a possibly life long friendship. That alone is already worth taking the first step and asking for time.
A friend recently asked me whether I am strategic about which people I stay in touch with. Honestly, not the least, I stay in touch with people who I genuinely like to stay in touch with. Some of them reciprocate this feeling and show me that they value the relationship with me as well, some don't. That's totally fine.
Imagine a world of relationships that you "strategically built" It sounds like a horrible world of fake advisors and fake friends which will likely reflect in your own happiness.

Slow down, progress not perfection
My last advise would be to take is slow. Nothing worth doing should be rushed. That applies to building new relationships too. Take it one step at a time and see where it leads. 
When I had a good chat with someone, I typically ask them at the end of the chat whether they can recommend anybody else I should connect with. Imagine the power of your network of people who you like, who like you and who help you uncover other people who they believe would be good people in your network. Real powerful stuff. 

Feel free to send this to someone who needs to read this and also drop me a note if you'd like to discuss further.