I've been running the same starter set group with 7 players for the last 2 years and we're almost finished the last cave. It was also the first time many of us had ever played - I'd certainly never ran a game before.
Here goes. It's going to be a long one...
Basically think in terms of action economy.
If there's only a few goblins, add a few more (though be wary of this before level 3 due to players max hp). If you misjudged and it looks like it's going south, have some of them "retreat for reinforcements". Matt Colville's YouTube videos are your friend.
One problem you may find (or maybe it's just my rowdy rabble) is a large combat can take almost the entire session. My group gets one decent encounter done, one room of a dungeon (more if there're no enemies), or a fair amount of role play - but never more than any one or two combined in a session.
If there's already a large number of enemies consider upgrading to their stronger versions. Make one of the Goblins a Goblin Boss, a Bugbear into a Bugbear Chief, etc. This will in turn provide better exp and actually get them levelling up in decent time, as your total is now being divided by essentially double the recommended amount.
I have to say I "upgraded" more than I "swarmed". Players get less bored and they get to level up more often. I'm always looking for the highest CR I can ever throw at them.
Which highlights another problem you may run into.
Instead of having a group of 4 guys at level 5 reaching the last dungeon, it'll maybe be 7 guys at level 3. Which you think may equate to the same thing, but I'd worry about their max hp. If they're going down in one or two hits you may have a lethal game of dominoes on your hands if you don't stock them with extra potions beforehand.
Third thing I found useful...
Have them do some extra side quests not in the book. If there's a cool Hydra mini you have lying around, have something on the quest board to maybe clear a Hydra out of a nearby swamp or forest? Making my own content seemed impossible when I first began, but the adventure lays good foundation for inspiration (and most importantly confidence) to sprout and take form.
Or have a Hill Giant or two attack the town - nice bit of foreshadowing for running Storm King's Thunder afterwards? ;)
Not keen on creating your own content? Well...
When in Thundertree, one player said "What's in that volcano? DM said the eruption was magical - there must be something cool up there!"
Oh, drat! What will I do? There's nothing in the book about that. I know! I'll run White Plume Mountain (from TftYP)! Why do they want to go in? I'll have a Fire Giant in the crater that can't get past the 1st riddle - he'll offer to smith them some obsidian gear if they can clear the place out (with the option of a double-cross when they see him again)!
They just turned level 5 as they entered (I gave them the exp for successfully negotiating a way past the FG without fighting him) and they just turned level 6 as they left - before a Copper Dragon lands, a fight between the two ensues and the players have to decide who to join in and help...
And all before Cragmaw Castle. Now they're halfway thru the final dungeon, now modded and far tougher than the one originally published (Skeletons become Wights, Zombies are Ghouls/Ghasts, etc.), level 7, only two of the original party left (they like rolling up new characters), many deaths, and many emotional moments. It's been a wild 2 years!
You just have to mostly play it by ear and get a feel for it. If you're new to DMing like me it'll seem quite daunting at first, but I promise you'll soon have a good feel for things before too long.
Sorry for such a long answer. I just saw someone in pretty much the exact same boat as me when I started. Hope it helps. And good gaming!