I'm trying to get a group together for a campaign. They've all already created character concepts, and all seem excited to join. The problem is, it seems like every day of the week, someone is taken, and I know that if we don't keep a consistent schedule, the group will eventually cease meeting. Does anyone know how to get everyone together, or how to break the idea that someone may have to drop out?
First determine if the game required the whole group to be present
I've heard that some games require that the group is consistent more than others (somewhere I've read that you should be careful in The Dark Eye for example because you need certain characters to progress past certain story points, but I've never played it), while others are more forgiving (DnD 5e for example). If your game doesn't require the whole group you can try to find ways around this issue, otherwise splitting your group might be better - run two games with smaller groups whose schedule alines nicely.
Handle absent group members out-of-character
This is something you need to discuss with your players, but often you can find ways to work around a few players that are absent. To give a personal example: I am the playing DnD 5e with a few friends. We are seven players plus me as the DM. This is a big group. We managed to get two introduction sessions where everyone was present so that I could teach them the basic rules they need to know to play the game.
Afterwards we changed the schedule a bit and stopped requiring everyone to be present. It just doesn't work, especially with so many people. During the week is difficult and everyone puts a lot of the personal stuff in the weekends, so we decided to play once or twice a month on the weekend as long as we get at least four players plus DM.
It's quite some work on the part of the DM to accomodate varying group sizes, but as long as everyone is on-board with the idea of changing the group size because "characters x and y are staying in the town to gather information while you are exploring the goblin cave" and "characters y and z came to the goblin cave last night and found you after they gathered information in the town" everything is fine. It's not a style that works for every group but for our group it does work and you might want to talk with your players about this.
Another idea we explored was to use Side-quests of one or two sessions length whenever there was only half the group and progress with the main story when everyone is present. It's important to decide on one or two sessions to have the time for a dungeon or little adventure arc, but then it's easily possible. For the side-quests you could just make a "quest-board" in the main town. Maybe you know that half the group will make it to the next two sessions and then the other half will be available, so sending them on "Orc extermination"-style quests might, depending on your group, be an option.
Try to find regular times to meet
Every other week on a Saturday for example. Or your alternate weekly between Tuesday and Friday. Try to come up with something so that everyone can be present every other session for example.
Work with milestones
You used "DM" in your comments, so I assume you are playing DnD. In DnD 5e you can also use the milestone rules for advancing. That way your players might feel better about being available only every other week, because the level-ups are given out after every big main-adventure story arc. Or maybe your group would like to progress as a group and it doesn't really matter to them whether the characters are present or not.
In my group this wouldn't work. I give out experience whenever they overcome some kind of challenge and they like it that way. It feels better to be rewarded instantly, but using milestones is nevertheless an option and might work for your group. Talk to them to find out how to do it.
Be prepared for drop-outs
If this is a first game as you mentioned in the comments then there is a possibility that some may drop out after a couple sessions, for example because they realized that there are more rules and difficulties than they imagined. Every new RPG is a completely new experience and every group has their own style. Devoting so much precious time to a game that is not quite what you were hoping for may have the effect that some people are dropping out. Of course you should talk to them and try to make the game something everyone on the table enjoys, but nevertheless someone may drop out. Which would make scheduling easier. So maybe you only need to find a schedule that fits for two or three sessions and then you can see how you want to progress.
Needs of the many outweighs the needs of the few
Your problem is one of the most common people out-of-school have: conflicting schedules. Find a day when you can get most people and go with that. Make a decision and roll with it, the alternative to one person being out is to not have a game at all, which is worse.
If you really want everyone to play, have you considered running two different campaigns (with player overlap)?
TLDR There is no one simple, unified answer (the others did post good advice...)
You could change the frequency and length of the game. Instead of a once a week on a specific day, have the game run at different intervals so that all players have to cancel the same number of extra activities. If it comes to that, you can run the game monthly on first weekend: both days, from 10:00 till midnight. Note that if your game is not regular, a good calender application is essential so players do not forget when the game is running.
It requires some planning and flexibility from your players, but worked really well.
Personally, all the games I run have a schedule posted in advance. If you cannot make that, you cannot be in the game. Tough.