It's pretty out there. I'll be frank the UNSC stuff won't be up to you, if you remember from the Model UN, non-permanent members have to be elected, so that's practically gobbledigook as a goal. You're more likely to get more leeway working for legislators and learning the ropes there than trying to set up some sort of crazy lobbying group on your own. There are already foundations that sort of do that like the American Pakistan Foundation:https://www.americanpakistan.org/
I'd say honestly you need to put in a lot more thought about a career trajectory that actually interests you and see what the real world positions are like. Lobbying means a lot of hand shaking and talking to people and legwork. It's a lot of budget wrangling and white papers and impact papers and negotiating with people on their terms and being an advocate for local issues first and foremost. You're not going to get to advocate for anyone internationally for a long while, even in the foreign service. The UN is a lot of rules and procedure and coordination, you don't really get to be dynamic there, you'll very much be a cog, that's how it works. The UN has an equivalent of C-Span that's worth checking out:https://media.un.org/en/webtv
Go to the UN jobs page, look at the job descriptions etc, go to the UN University site, look up some IR/Public Policy journals (your local public library will let you have access if you want to be legal and don't have access to your college library anymore warna Scihub zindabad), go to talks at universities, pound pavement, email people, 1 out of 10 of them will reply to you, and if you're lucky more will. But yeah, get a Master's in Public Adminstration/Policy. The only catch is that those tend to be economics focused so there's a bunch of statistics involved nowadays which you'll have to brush up on, and that's something you want to lean into, because it's the largest growing part of public policy/administration sectors and it'll be unavoidable in a few years.
At the very least you'll want to learn some scientific computing:
https://www.freecodecamp.org/learn/scientific-computing-with-python/#python-for-everybody
And once you brush up on the math a little then:https://www.freecodecamp.org/learn/data-analysis-with-python/
Pick up a course on R because it's the go to data mining and wrangling tool in general in academia now. If you're not a math person it's a little hard to get going but it's almost a necessity to have some data mining skills in public policy programs these days, so you should start soon:https://www.codecademy.com/learn/learn-r
https://www.coursera.org/learn/r-programming
https://www.datacamp.com/community/blog/how-to-learn-r
https://youtu.be/_V8eKsto3Ug
If you're not a statistics person, don't worry. It's better if you are, but you can get away with just knowing how it's being used, which unfortunately you'd still have to learn so you can assess work or read off databases, how data visualizations can be flawed, what a table generally should look like, how to assess margins of error and how to talk to colleagues about it. The future of public policy and administration is data though so you might as well bite the bullet and do the work. Don't get me wrong, being a strong writer is still important too.
This is a good book to get started, assuming you follow up on some of the more complicated math yourself: https://www.amazon.com/Practical-Research-Methods-Nonprofit-Administrators/dp/0205639461
You can find it on Library Genesis easily. If you wind up in a government job it won't matter as much in the US, they have number crunchers specializing in that, but if you're working for lobbyists, NGO's, want some say in making decisions in the future, this is necessary now or at least is going to be something you're assessed for over the next ten years. Gone are the days where you got a PoliSci degree to get into a public policy or IR job, outside of academia. I don't think LinkedIn even has PolSci as an option anymore.
Also the r/PublicAdministration subreddit maintains a Google Drive with great books worth browsing, although you'll have to find a lot of it yourself, since some of it is just reviews or links: https://drive.google.com/drive/folders/1VD1HlUdX3RAyWGQ8x9vLQirtAkA-i0_D
Or you know, you could do your masters, get a job, do your CSS (remember you have to be under 30 when you take the exam) and climb the ranks in Pakistan. If you do good work the world's getting more complicated, and it's going to get harder and harder to be incompetent in government without horrible results. With the sort of data driven policy in our future you could be a pioneer here, and it'd be far more accountable than it used to be by its very nature. Good luck.