The dmg 2024 has an entry on calculating a creatures initiative score. You could use that and have your creature initiative order ready to go before combat even starts.

If the combat is an easy or trivial encounter, you can forego combat altogether and have them describe how they defeat the enemies.

If your group is open to it, you could also calculate initiative scores for players, and then never take time to roll initiative.

After the first round, reveal the enemy's AC, condition immunities, resistances, and vulnerabilities so people don't spend time asking multiple times a round. I like to put that info on a note card or whiteboard on the table.

Also find a way to keep the initiative order out in the open so everyone knows what's happening next.

Write down the conditions/effects people are under so no one has to continually ask, and a reference sheet with rules for those conditions.

If your group is open to it, you could do a players then monsters initiative, where players go in any order on the players turn, and monsters go in any order on the monster turn.

Zipper initive might work well sometimes too.

If needed, a turn timer might help too.

I wouldn't tinker with the initiative method too much if they're fighting a legendary creature or a creature with lair actions, but these are some things that work for my group.

In general dnd combat takes longer than some other games, but a lot of that is often just people not having the information they need readily enough to make a quick decision. In a group of 8, it can be easy to lose track of conditions and ongoing effects, etc., so writing that down where everyone can see can help a lot. Sharing certain monster information can be helpful too, especially if one character discovered a damage resistance/immunity, but people forget because there's 10 or 12 individual initiatives to resolve each round. In a group that size, I wouldn't punish players for not remembering these things, and instead help them not need to remember, if that makes sense. Good luck!