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I have data stored in a firebase realtime database, in the following format.

users:
 -L5ZAb7r10_nqss7Ag:
 role: "user"
 email: "person@example.com"
 username: "King Arthur"
 -KL3Abnar7_nals8:
 role: "admin"
 email: "other@example.com"
 username: "Queen Ferdinand"

And in the database.rules.json I have:

"users":
 ".indexOn":["email"],
 ".write": false,
 ".read": "auth != null"
,

On the front end I have a user giving their email, having been authenticated with Google OAuth, and I want to see if their email is a valid user, and if so return their role and username, otherwise throw an error. Right now I loop through the 'n' accounts and check each account's email. O(n) is obviously a really sucky runtime.

Not knowing what the user's key in the database is (the "-L5ZAb7r10_nqss7Ag" part), I want to be able to check for the given email in O(1) by searching the email in the indexed database. What I have in mind is something like the below. If this is posisble can someone point me to the riht documentation for the correct syntax?

firebase.database().ref(`/users/`).getIndexedValue($key/person@example.com).once('value').then(function(snap)
 if(snap == null) console.log("error);
 else
 user = snap.val();
 console.log(user[role]);
 console.log(user[username]);
 

I know the above won't work, .getIndexedValue() isn't real. What would be the correct syntax for this functionality? Is there someway to look for a specific indexed value (the email) that sits below an arbitrary partent (the -KL3Abnar7_nals8)?

You're looking for orderByChild() and equalTo(). Something like this:

firebase.database()
 .ref('users')
 .orderByChild('email')
 .equalTo('person@example.com')
 .once('value').then(function(snapshot)
 if (snapshot.exists()) 
 snapshot.forEach(function(snap) 
 user = snap.val();
 console.log(user[role]);
 console.log(user[username]);
 )
 

To learn more about Firebase Database queries, see the documentation on sorting and filtering data. I'd also recommend checking some previous questions on the topic.