Sounds great, Leandro! Are you all eating out, or at someone's house and whose? I had several "first family dinners" with hubby's large family, as I met a number of them in smaller groups at different times. All there knew we were gay lovers, so we didn't have that to conceal. One was at a restaurant, one at a home during a big "family day" gathering, and a couple at my partner's sister's home, one of which included a birthday party for a young relative.
His parents are gone now, but his surviving sister & brother are the most important in the whole family, especially the older brother who's like the patriarch. And a grumpy old homophobe at times I was told, that some were afraid of. So naturally I targeted him for special attention, and talked antique cars with him, which I had learned were a big hobby of his. I think a gay guy talking knowledgeably about cars surprised him. We're good friends now, talk on the phone, he invites us both to his vacation place down here, always insists we have dinner together with them when he comes down from out of state.
I suppose the one thing I did at the home dinners was to ask how I could help, which turned out to be taking over the drink duties for everyone before dinner, while the host(s) remained busy in the kitchen. Not sure if any of your family will drink and your BF is comfortable mixing simple cocktails, but even serving Cokes works.
The idea is for him to be seen acting almost like family already, in a comfortable interactive situation, doing his part to keep everyone entertained, attentive and gracious. The conversation will flow from there.
And BTW, since I knew my partner's sister loves formality, even doing tent cards at each place setting, I offered to provide cards I designed & printed from my computer for our first dinner there. She was thrilled when I brought them, telling everyone who had done them, only now I still have to make them for every one of her dinners ever since. She phones or emails me the names, and I have to get the cards up to her place some 30 miles away. Oh, well, that's what happens when you become family...
At the restaurant, which this different set of family members knew & liked but I hadn't been to before, I made sure to compliment their choice of places, and consult them about the menu items. As with serving the drinks, "functional interaction" is a great way to get to know people and to bond in a natural way, without resorting to awkward forced conversations.
Also, before dinner my partner & I (I think still just BFs then) had privately discussed how we would handle the check afterward, and if I should get bottles of wine for the table, and so forth. He knew his family's habits and preferences, and it's better to have some of this "rehearsed" beforehand to lessen the chance of any clumsy moments later, especially regarding money. And naturally we both made sure we had plenty of cash & in what amounts, for valet parking & tips, etc, and our cards with us.
Well, that's quite a lot of words, if not too much specific advice. On the matter of general socializing skills I'll assume you guys know those already. Good luck and have fun!