I don't work in Tech, but I was a HR Director for a considerable length of time, so for your own benefit OP, I'm going to point out all the pitfalls of this post in what is probably a futile effort to instill some sense of professional growth in you.

My goal is to get to management as quickly as possible.

While admirable, there's a pretty big gulf of knowledge and responsibility between being a manager and a member of the team. The attitude is different, the expectations are different and the ability you have to interface with people on a professional level within the corporate climate usually takes a few years of acclimation.

You're also making a pretty base assumption that there's even an opening for another manager, and that, despite your relatively short tenure, you're somehow more qualified with people that have been at that company longer than you. In a promote from within environment, you're at a disadvantage; in a promote from outside situation you're not even a contender without some pretty ground breaking work. Even if you are a candidate promotion, do you have the skills to handle subordinates younger than you with your same attitude, or those older than you who totally eclipse you in technical/corporate knowledge?

In our first meeting, I told him that my goal is to get promoted at the end of the year. He said that's not possible per some company policy (not true), acknowledged my ambition, and gave me some next steps. To my dismay, most of them were bug fixes or small unimportant tickets. I went back to him and asked for higher visibility or re-architecture work and he basically dismissed my concern and said it takes time.

I'm overwhelmingly curious as you know how this isn't true. Aside from the assumptions about positions, etc., by promotion do you mean a raise? This is a pretty big red flag for anyone in a managerial position as you're making an assertion that you already expect more money for what you're doing, despite having not actually done anything worth getting a promotion for, you're already, less than a year in, looking down on your assignments as they are somehow beneath you. This isn't a good precedent to set. Your manager handed you an opportunity to show him what you can do, be that efficiency, quality of work, etc and you chose to scoff at it (this isn't a good look).

To his credit, he later offered to add me to some architecture and design meetings to see what they're like. I spoke up, asked questions, and gave my recommendation like others but my manager kept shutting me down with "let's take that offline" or "I'm happy to sync up with your question afterwards". When the rest of the room went quiet after I said something, my manager certainly didn't step in to support me either. To make matters worse, he later criticized my initiative and told me I needed more context before I could give recommendations to a wider audience. That might be true for others, but I grasp technical material very quickly.

This was a pretty major opportunity for you to do that 'acclimate to corporate culture thing', and you blew it. He brought you there to show you who else was working in the department/on the project and for you to get a glimpse into it, not for some fresh faced new ideas that totally haven't been iterated on already or brought up in the past. He, very politely, asked you to shut up, and you didn't. Bravo.

From there, it's just been downhill. Not only does he no longer invite me to those meetings, but it's clear he thinks very little of my technical skills. He shared our 1 on 1 meeting notes and he wrote "... needs further opportunities to dive into node". Except for the fact I told him that I've already used node through most of school and previous internships.

Yeah, he brought you to the meetings to meet people and take notes, not to be disruptive. This was probably a reward and maybe an acquiesce to be considered for promotion at a later time, and as previously stated, you messed this up (and probably embarrassed him, I feel like it's safe to assume you didn't apologize for you behavior in the meeting)- of course you haven't been re-invited to additional meetings.

My review score was an N/A because he said that's what everyone got their first partial year. I'm pretty sure that's complete BS. He has a track record of growing and promoting campus hires, but none of my race and gender combo. I've asked my teammates if they've noticed what's going on and they either don't believe me at all or agree with him. It's fucking nuts. I scheduled a meeting with his manager to express my frustrations and was basically told that she appreciates my enthusiasm but agrees with my manager.

First, review scores vary company to company, some won't give a score if you've been employed for less than a year, some will. Have you considered talking to HR to verify this, or are you just going to make an arbitrary decision based on corporate policy you know very little about? Either way, it's not like you can demand a score, and there's a good possibility that it's policy.

Second, I don't understand why you just won't admit that you can be at fault sometimes, you're seeking validation in your co-workers and their confirming that the problem is you, and not with the manager, who seems to be, in my opinion acting in the best interest of his team and the company.

What should I do? It's clear that my manager is young and inexperienced, so he likely doesn't know how to handle the situation or young talent. I'm thinking I can escalate to his manager's manager, talk to HR, or try to switch to one of the other teams but I'm open to suggestions.

Escalating this to your manager's manager isn't going to win you any points- with anyone. You're going to be the difficult employee, you're poisoning the well for yourself, and HR is/has already written the conflict resolution strategy for your termination. There's a saying in HR, and that's 'HR and Managers don't fire people- people fire themselves'. It's quite applicable to your situation.

I hate to be the one to tell you this, but HR doesn't exist to take care of the employee, it exists to protect the company. If HR finds in the managers favor, what's your plan of action? If HR finds in favor of you, what's your plan of action? Really, what are you going to do? What have you gained? Do you think you're any closer to promotion or even consideration for promotion after this?

Your best hope at this point, and I really hope you read this, is to submit to the will of your team. Do the work you've been given, apologize to your manager for your post-graduate 'gusto' and stop making arbitrary correlations between a proven and well-liked manager and your peers based on your own personal work ethic and social short-comings. Seriously, do everything you can to salvage your reputation at this company, because the one thing people like you who inevitably hand-wave all this advice and make weird talking points about their 'alpha personality traits' is that people talk to people. If you burn this bridge, be prepared to embrace the idea that you're probably not going to a different team, and you're probably also not working for a different company that someone who came up with this company is now working at.

I wish you luck, dear redditor, you're in for quite a journey.