There are many options, and I will recommend the following based on my experiences as a player and DM:
1. Be a team leader instead of just being one of many people.
This is probably the broadest solution you can use as a player. I have used this to attract less assertive or less interested players. Your contribution does not need to be an announcement of what your character will do alone; It can also be something else in the line of organizing other characters in a plan that the group carries out.
Whatever the challenge, you can let each individual do their own thing and expect at least one to succeed. OR You can prepare a plan in advance, specifically suggesting actions or asking players to contribute:
Okay, we have to convince Lady Obstacle to allow us to use her invitations to the Lord Villain's grand plot dance so we can complete the search. Alice, you have high statistics on Persuasion and History, maybe you could talk to her and remind her how deep the enmity is between House Obstacle and House Villain, suggesting that she may not want to go to your event? Or Bob, you're a bard that you liked before, is there anything you can think of that might influence her?
Very artificial, in this example, but this allows you to fight for space in the conversation, and then offer it to less assertive players to give them a clear opportunity to participate.
If you like to plan things, you can also try to persuade some of the firmer players to take some course of action that leaves other things for the other players to do, giving them more space to participate by eliminating the most dominant players from the scene.
At a minimum, you can ask other players what they think or would like to do. That is very easy to pass in and out of the character.
2. Make plans that require specific characters, which less aggressive players play.
As more than a subset of (1), if you come up with a plan that your own PC can carry out but would be helped by the participation of one of the less firm players, you can give them moments to get involved and that otherwise they would not find . Being helped by another character to gain an advantage can have a strong effect on the results, and the contribution can be quite obvious (if your first roll is a 3, the advantage clearly matters). One risk of this is that some players may feel like partners, so this tactic works best if it is uncommon.
3. Divide the party
This is a nuisance in many ways, so it is also best to use it in moderation, but getting the dominant players out of the scene occasionally gives others the opportunity to play "normally" without being discussed and ignored.
4. Talk to the DM
Making sure everyone has fun is a central responsibility of the DM, and if some players are running over others to the extent that they are not playing large sections of the game, that is a problem. The DM has many tools to address this type of situation, perhaps the most important thing is to ask the players what their characters are doing. They may not have anything in mind, but they will have the opportunity to speak.
I have also read advice on this stack that suggests that, out of combat, all players announce their planned actions before the DM resolves any of them, but I have no personal experience with the use of this technique in this type of problem. An infallible approach is to design a plot for specific characters, since such things can not only be transferred to a louder player, but can be expensive for the DM plan and managed with such a large group.
5. Talk to the group
Some of the most assertive players may not realize the effect that their focus is having on some of the other players. They may or may not care about the problem, but mentioning it gives everyone the opportunity to meet and discuss the answers they deem appropriate.
A particular dimension that I think is relevant is that players who are more assertive or arrogant may not be so interested in sitting on their hands, so if you spend too much time without something for your character to do so, they may become even plus assertive and dominant. Noting that greater participation for them could mean much less for others provides a context of why it might be worth leaving them aside for a few minutes.
It also happens that some players don't really to wish Being in the driver's seat for this kind of thing. They may prefer to aim at a monster and then let go, and they don't mind devising a free-form plan to deal with another NPC. Talking with the group can reveal if this situation is really a problem for quieter players. It may be, but it could also be how they want to play.
6. This is a large group, and there will probably be some give and take no matter what
Seven to eight people is a lot of people who will gather around a table for a role-playing game. It takes a lot of real time to analyze the actions and thoughts of so many characters, often with the effect that the game slows down. It is often not feasible to have 7-8 plans running at the same time, or have people take in 7-8 different directions.
Sometimes it may be desirable to let some characters do little for a scene or two just to simplify things and advance the game. That becomes a problem if it happens all the time and with the same characters, but only by perspective, totally equal contributions in all cases may not be what you want.
Once I tried to run a D&D 3.5e game for ten players at a time and this was a big problem. More players means more competition for the short time in the camera, because while the number of players can increase freely, the amount of time people have to devote to games generally does not.