CSES standard solution for range query problem giving TLE Problem statement is from CSES
This is a standard question where we are given a list of numbers and a number of queries. For each query, you have to give the sum of numbers in the given range.
My implementation in python:
def solve():
    n,q = [int(a) for a in input().split(' ')]
    arr = [int(a) for a in input().split(' ')]
 
    cumulativeArray = [0] # Initial entry added to make 1 based indexing
    sum = 0
    for i in range(len(arr)):
        sum += arr[i]
        cumulativeArray.append(sum)
 
    for i in range(q):
        x,y = [int(a) for a in input().split(' ')]
        print(cumulativeArray[y] - cumulativeArray[x-1])
 
solve()

This gives the required answers correctly for all my custom test cases. But gives TLE for huge test cases.
I believe this is happening due to split() method in my code.
Any leads are welcome.
You are already using the optimal solution algorithm for the problem. A few things, which might speed-up the computations (.split should not be the limiting factor in most likeliness)
Variable naming
Use names which match the problem description, so that it becomes easier to follow your code. So, instead of x, y it'd be a, b. Also, in python, it is a good practice to name your variables in lower_snake_case.
sum is an builtin function. Do not override this.
Computing len
You do not need to iterate over indices as the index is not really being used anyway. Lists can be iterated over their values itself.
Lazy iterators
Instead of generating list inline, you can use generators so that the values are yielded when iterating, and not consuming memory.
.split
Not passing a parameter to .split is same as providing whitespace as parameter.

Rewrite:
def solve():
    n, q = map(int, input().split())
    arr = map(int, input().split())
 
    cumulative_summation = [0]
    running_sum = 0
    # Not calculating `len` of `arr`, also, you don't need to calculate it.
    # the length is known to be `n`.
    for value in arr:
        running_sum += value
        cumulative_summation.append(running_sum)
 
    for i in range(q):
        a, b = map(int, input().split())
        print(cumulative_summation[b] - cumulative_summation[a - 1])