Checking for an existing user in a database return user if exists return false if user does not exist

There are many things to mention here:

1. I recommend using an ORM like SQLAlchemy together with Flask. It will make your life a lot easier and you won't have to worry about some security issues (such as SQL Injection).
2. If a user is going to log in, it is a good practice to return the message "wrong credentials" if their email OR password is incorrect, so an attacker will not know which one is correct or incorrect, therefore they will have many, many more combinations to try. That is, by just changing the phrase "wrong password" to "wrong credentials" you will be covering a security hole in your application. The same message should be returned if a user is not registered.
3. I recommend reading up on the uses of underscore in Python, since you are apparently using it in a place where it isn't needed.
4. In Python you don't need to use getters and setters unless you need to do some preprocessing before getting or setting an attribute.

Finally, in Flask this is a common way to structure a small project:

__init__.py

from flask import Flask

from utils import get_db_connection


app = Flask(__name__)
db = get_db_connection()

utils.py

# Do the necessary imports.


def get_db_connection():

    ...

run.py

from . import app


if __name__ == "__main__":
    app.run()  # You can set multiple settings in run().

routes.py

from . import app
from user import User


@app.route("/login", methods=["POST"])
def login():

    user = User.get(request.form.get("email"))

    # This is not recommended.
    # if not user:
    #     return redirect("/register", email=request.form.get("email"))

    password = request.form.get('password')

    if user and user.check_password(password):
        session['userID'] = user.id
        session['name'] = user.first_name
        session['email'] = user.email

        return redirect("/user_index")

    return message("Wrong credentials. Go to log in page to try again.")

models.py

from . import db


class User:

    def __init__(self, id, last_name, first_name, email, date_of_birth, hash):

        self.id = id
        self.last_name = last_name
        self.first_name = first_name
        self.email = email
        self.date_of_birth = date_of_birth
        self.hash = hash
    
    def check_password(self, password):

        return check_password_hash(self.hash, password)
    
    @staticmethod
    def get(email):

        user_result = db.execute("SELECT * FROM users WHERE users.email = ?", [email]).fetchall()

        if user_result:
            return User(user_result['id'], user_result['lastName'], user_result['firstName'], 
                        user_result['email'], user_result['dateOfBirth'], user_result['hash'])
        
        return None


# Declare more classes for your database models!
# class Admin:
#
#    ...