1) The Borg open a big rift in space and call out from it ominously in a thousand different languages that they want to join the Federation. And more than that, they are asking Picard specifically for help. This M.O. is so far beyond what the Borg usually attempt that something has to be going on here beyond typical Borg doing bad things. Especially when the Borg are characterized as broken and scattered - implying Janeway's victory over them during the events of "Endgame" was a veritable death-blow.
2) Knowing the Borg M.O., and that if you give them time and opportunity to adapt, they will, I think it's safe to assume that standard procedure when encountering active remnants of the collective here is to shoot on sight. Especially when the Voyager came home with Borg-defeating tech. If the Borg manage to ever assimilate that stuff, the UFP and the rest of the Galaxy are potentially screwed.
3) The Borg's entire motivation for what they do is to 'seek perfection' though assimilation, but they're also governed by logic and reason. After getting their asses whupped by the Federation over and over, and them not just hitting a wall in their evolution but getting dealt crippling setbacks, at what point do you finally 'adapt' by reassessing your methods? Wouldn't you begin to wonder, maybe the Federation's method of 'assimilation' to be superior at some point? And if that's the case, wouldn't the logical next step then to be to join them? Since they have a history of including once bitter rivals among their ranks, and you can ride their coattails to perfection?
I could be wrong, but all of this that I just laid out really feels like their request to join the Federation is likely in good faith/honest/earnest. But what's that got to do with Picard's mother? Well.
4) Consider the immense amount of ill will the Collective has earned itself over the centuries. Consider what I laid out previously about standard operating procedure for the Federation dealing with the Borg - shoot first, ask questions later. If you're the Borg, in order to get to the bargaining table, you have to figure out a way to get the Federation to sit down and listen instead of just blowing you up the second you arrive.
5) And that's where Picard comes into play. He was once the collective's point of communication for the Federation when it tried to assimilate it. They know his mind, history, and thought processes intimately. And while there are numerous former-Borg, he's the one in the highest position in Starfleet to affect change and has a legendary history as a diplomat. If you stand a chance at appealing to anyone, it's gotta be him, right? They don't know how Admiral Janeway's mind works, Seven is in no position of authority, etc, etc.
6) The Borg show up in a giant ship that's unlike any of the ships we've seen them employ previously. It only has bilateral symmetry, versus being a classic geometric shape. And it opens up like a giant space vagina. (sYmBoLiSm) The Queen shows up in regalia and clothes, affectations that are completely illogical to the Borg we know, and would be pointless for the sake of malevolent subterfuge. This is our first clue to the Borg Queen's identity. Go back to the first episode and examine the Borg Queen's cloak that she's wearing. It's a color and has patterns on the shoulders that visually evoke the exact same jacket that Picard's mother was wearing in the flashback of his childhood that he remembers. That doesn't feel coincidental.
7) The Borg Queen begins taking over the ship, but consider her actions while doing so. The last thing she says before she begins the takeover of the Stargazer, is she says - almost like an announcement - that she needs power first. So she begins draining the ship's power and taking over the ship's command systems. Which would feel nefarious in a vacuum, but upon examination feels much less so when you add the context of what else is going on. She puts up a shield that is almost passive in nature. It protects her and only stuns the security officers coming to subdue her, not kill or vaporize. If taking over the Stargazer and thus the fleet for nefarious purposes was really the Collective's intentions, then logically speaking she should have murdered everyone in that room so as to not give the command officers a chance to thwart her plans. But she doesn't and allows the auto-destruct sequence to play out. I've already stated that I believe the Borg's stated intentions were probably honest, and this is what does it for me. But there's even more clues here to explore.
8) The Queen is drawing power from the ship. She states it as a necessity. When we see the Confederation Timeline Queen, she too needs power to reenergize after guiding the ship back to the past or else she'll basically shut down. Taking over the ship might just be a security thing the same with the shield, but drawing power might be a legitimate need instead of just metaphorical power of taking the ships over. And I bet opening that rift in space took a lot out of her.
9) The Collective is asking for help, and is acting with abandon and urgency, in ways that feel utilitarian and Borg-like, but also betray legitimate attempts at diplomacy. Cryptically alluding to being "out of time." If we are to continue to take their request at face value, their urgency has meaning. Remember that Borg Queens are sensitive to parallel universes and shifts in the timeline. One of the ways changes in the timeline is characterized in Star Trek previously is that there's a certain delay that occurs when a shift happens. If the 25th Century Queen was perceptive of an impending change in the timeline due to Q's interference, wouldn't that suddenly make a lot of what's going on make even more sense? After all, this just went from "we want perfection" to "we want to survive". And Picard's intimate knowledge and personal relationship with Q would even further make him an ideal candidate for contact.
But here's the real kicker to me, that wraps everything back into my thesis:
10) When Picard is in the middle of giving the Self-Destruct commands, the Queen begins playing "Non, Je ne regrette rien" diegetically throughout the ship. The same song Picard's mother loved and would play to him as a child. It's almost like a final plea before he enters his command codes. Again, why not shoot the man instead of pleading to him like this in such an intimate way? Picard goes through with the command codes, and the ship is just moments from being destroyed, and nobody can stop it. The Borg Queen addresses Picard directly and calls him by his human name. Not Locutus like they've condescendingly dead-named him in the past, but in a way that recognizes and honors his identity. Their fate is sealed, and any actions taken during this moment are essentially meaningless. And yet she approaches him and tells him one last phrase. "Look up." Really go back and listen to how that's said. It's no longer in the synthetic, Borg voice, but done clearly in a regular intonation. And if you listen carefully and compare back to the beginning of the episode, it's being said by the actress who played his mother Yvette. Picard's face does all sorts of delightful contortions displaying confusion in his final moments. Because those words have meaning to him. He said as much at the beginning of the episode. They were the very words his mother would inspire him with that propelled him along his entire life trajectory.
So for such a utilitarian species that prides itself on efficiency and logic, why evoke such an intimate and personal memory to a man about to die? That's the thing I keep coming back to, and is something I both rarely see commented upon or even observed, and that I can't really reconcile with any other explanation.
The hood veiling her face is so that she doesn't immediately startle and raise the suspicions of Picard upon their first encounter. But I can 100% see the Borg invoking Picard's mother - his memories of her and her form - as the final key that makes the entirety of the opening scenario to make sense. Picard's mother was his inspiration for his entire life. She represents to him the best aspects of humanity. She informs all of the good in him and all of the optimism and faith that defines the limitless potential of humanity. And yet, at the same time, she is also implied to be the source of Picard's greatest trauma. Growing up in a broken home where his father beat his mother. A trauma that cut to the heart of his personage so deeply that it led to him joining Starfleet not just to go explore but to run away from his problems at home. That informs all of his intimacy issues that so relatably mare his desires to seek companionship and love -- what if I end up doing to my paramour what my father did to my mother? Coming to him personally, in that form, in that voice, saying those words. Are the actions of someone who wants to connect - to reassure that I understand you, that I am here not to harm but to love. I know you, you can know me, this is how I feel about you. We can have peace and coexistence. Let's help each other. Let's become better together, earnestly in ways that respect one another.