I feel like each character having two other connections would be a good number to aim for. I mentioned the miner-smith relationship with Topaz, but maybe I can add a few others now that more characters have been posted. It being winter actually gives some topic of conversation since Cami is from Neverwinter. Meaning she's used to a warmer climate throughout the whole year, and that's about it.

• Vyrax. I think the idea of stealing here is fine. Cami is True Neutral taken to an extreme, so she has no trouble forgiving him once she has received her things back, but I have no idea how to align the duo's motivations together.
• Tanlen. Honestly, it's a bit hard with only the information I have right now. He came from the Underdark, and he was the bodyguard/face of a trade caravan. The best I can give you is that Cami is a curious mind, so maybe she'd look for someone on Underdark knowledge to advance her studies?
• Ianric. A bit similar to above. Cami is inquisitive, so if the two as much as passed by each other, she'd be looking to know more about whatever happened to him. Seeing as he's so eager to tell people, I don't think it'd be too hard for it to become a connection.

I agree, the miner-smith thing sounds great for Topaz/Cami. Topaz would've also been open to hearing about Ianric's story, met Tanlen in an underground mine tunnel, and gladly listened to Vyrax's songs.

So here's what I've got so far:

Topaz and Kassar - met in the sewers while Topaz was on his way to meet a buyer.

Topaz and Cami - work associates, help each other with material.

Topaz and Vyrax - Topaz likes his music, and may have been robbed/nearly robbed by him.

Topaz and Tanlen - met while Topaz was mining underground.

Topaz and Ianric - Learned of his stories (Perhaps through Vyrax?) and is curious about him.

Cami and Vyrax - was almost robbed by him, but now they are cool.

Cami and Tanlen - Cami is curious about the Underdark. Perhaps met through Topaz?

Cami and Ianric - Cami is curious about the predicament of Ianric's condition.

Vyrax and Ianric - Vyrax is trying to find any truth behind Ianric's claims, and may also want to write a song/story about him.

 If I need to edit any of these connections let me know.

Looking at all of these, it almost seems like Topaz is the mutual friend of everyone in the group. Maybe you're all coming out to the Yawning Portal to celebrate something for Topaz? His birthday, maybe, or perhaps he's struck a deal with a buyer and has some extra cash and he'd like to treat everyone to some drinks?

I'll add more after work, today is busy and I am only really able to get on since this is my break.

Not a problem.

Forgot to mention, I do plan on using milestone leveling for this game. I don’t have many homebrew rules for games but I do treat drinking healing potions as a bonus action (action to administer to someone) and use Mercer rules for resurrection. Let me know if you have any issues with that. 

Additionally, I’ll be using some stuff from DM’s guild that adds a little more content to various parts of the adventure, so if you’re familiar with Dragon Heist, there may be some additional stuff in this version I’m running. 

Okay, an idea:

Topaz is celebrating something at the inn. He invites Kassar, Tanlen and Cami.
Ianric has been almost a regular customer at the Yawning Portal (or perhaps, if there are rooms in the tavern, it's where he's staying?) and Vyrax is there, following him.
Vyrax is playing or singing for the tavern while the others enter. To his embarrassment, Cami is there. The problem with Cami is how she just forgave him and continued as if nothing happened. As a Tiefling, and a thief, he's used to being chased/yelled at/reported to the guard or something similar. He doesn't really know how to process this.
Vyrax tries to avoid Cami's eyes and, when his song is over, he goes and sits by Ianric.
Unfortunately for Vyrax, Cami follows him as he steps down from the stage/chair/whatever and her eyes fall on Ianric. She becomes curious about the pink Goliath and decides to approach, asking Vyrax to make an introduction between the two. The others look at Cami, perhaps following her once they also notice the strange Goliath. (Another option is that Topaz makes a remark about Ianric that shows his interest in the Goliath and Cami tells him that she knows the Tielfing sitting by the Goliath that is speaking to him and suggests she'll ask them to make an introduction.)
Vyrax decides that, if it reached this situation already, he should make the best of it, and conducts the introduction. After that, he hopes to be able to show Cami his better side - that he's more than just a thief. Even if she doesn't care anymore. He might stray to theft from time to time, but he isn't really proud of it. Moreover, he doesn't want that fact to hinder people's perception of his music, so he wants to make sure Cami doesn't feel like telling the others about it.

Now everyone is together in the inn, getting acquainted, ready for the beginning. Thoughts?

Yeah, sure, something like that is fine by me. Anyone take any issue with that?

Sounds great!

Works well enough for me.

Seems legit. I'm thinking a color lighter than this for Ianric's skin tone, and also if no one has any issues it'll be the color I have him speak in. 

Does everyone have a Roll20 account? If not it’s free to make one. I’ll set up a campaign, post the link in the DDB campaign page, and handle issues of combat maps and such on there. 

Does everyone have a Roll20 account? If not it’s free to make one. I’ll set up a campaign, post the link in the DDB campaign page, and handle issues of combat maps and such on there. 

I've got one.

Gotta write this again since the site had some sort of error.

The way it is planned works for me and now for a bit more of the backstory.

Tanlen was born in the ruins of the deep gnome Bligdenstone, his people having returned years after the crow ransacked it for revenge for a battle in the past. In order to gather resources they began to rebuild old trade routes to the surface, specifically to Waterdeep. Once he was considered old enough, Tanlen joined in on both trading and mining expeditions.

During a routine expedition they came into conflict with a group of goblins, the gnomes easily overtaking them. In the aftermath of the battle, Tanlen came across a strange spear that seemed to have been calling to him. As he picked it up a vague promise of power came into his mind, a deal being struck as his hand fully wrapped around the weapon. Soon after he found that he had a small amount of magic he could call upon, the weapon sending him scant emotions to show its approval or disapproval. Not knowing what to make of it yet he continued on with his life, soon going to Waterdeep on a trade expedition.

I find it interesting in certain regards. Namely, Cami has the worst Charisma of the party, and she tends to introversion, but you nailed her down on the information I had provided beforehand. It's just a matter of changing the order a bit.

She saw Ianric the moment she walked into the inn, but she only went to talk with the Goliath once she noticed an acquaintance of hers was sitting with him.

Just characterizing Cami better, so people begin to expect the right kind of character out of her.

Quote from MightyOwl >>

Does everyone have a Roll20 account? If not it’s free to make one. I’ll set up a campaign, post the link in the DDB campaign page, and handle issues of combat maps and such on there. 

I didn't even see this when I posted last, but now that I've seen it. Here's the answer. Yes, I have a Roll20 account already.

Quote from MightyOwl >>

Does everyone have a Roll20 account?

  Yep, good on that.

Aye I have an account. I just haven't used it in a good while.

I do but haven't used it much.

It's pretty straightforward to use, but if you have any questions as they come up during the game feel free to ask me or one of the other players familiar with the program.

I have posted the link in the campaign page so feel free to join.