Как иметь переменное количество пользовательских входов на основе первого пользовательского ввода

Вам нужно использовать петлю. Я удалил try/except, вы можете добавить его обратно, если хотите.

def student_average():
    number_of_qualifications = int(input('What is the number of qualifications?: '))
    sumx = 0
    for _ in range(number_of_qualifications):
        sumx += float(input('What is the next qualification?: '))
    return sumx / number_of_qualifications

print(student_average())

Я изменил ваши коды, поэтому функция try-except сохранена.

def student_average():
    total, c = 0,0
    number_of_qualifications = int(input('What is the number of qualifications?: '))
    while True:
        try:
            # I want to create inputs depending on the user's input in the following question:
            total += float(input(f'{c+1} What is the qualification?: '))
            c += 1
            if c == number_of_qualifications:
                break
        except:
            print('This is not an option')
    average = (total / number_of_qualifications)
    print(average)
    
print('Average of students')
student_average()

Выход:

Average of students
What is the number of qualifications?:  3
1 What is the qualification?:  4
2 What is the qualification?:  5
3 What is the qualification?:  a
This is not an option
3 What is the qualification?:  6
5.0

Пожалуйста, не используйте «сумму» в качестве переменной, потому что это зарезервированное слово Python. Если он использовался ранее, вам необходимо перезапустить ядро.

def student_average():
    cnt = 1
    total_list = []
    number_of_qualifications = int(input('What is the number of qualifications?: '))
    while len(total_list) < number_of_qualifications:
        try:
            # I want to create inputs depending on the user's input in the following question:
            total_list.append(float(input(f'{cnt}. What is the qualification?: ')))
            cnt += 1
        except:
            print('This is not an option')
    return (sum(total_list) / number_of_qualifications)
    
print('Average of students =', student_average())

Выход

What is the number of qualifications?:  5
1. What is the qualification?:  10
2. What is the qualification?:  20
3. What is the qualification?:  30
4. What is the qualification?:  aa
This is not an option
4. What is the qualification?:  40
5. What is the qualification?:  50
Average of students = 30.0