Algorithm for Cumulative Maximum with First Element Removal

I am trying to implement a data structure for storing the cumulative maximum (cummax) list of a given list of integers with efficient remove-first-element operation. In a cumulative maximum list an element at index i is determined as the maximum number among all elements in the given list with indices less than or equal to i. For example, for the list [10, 7, 8, 0, 3, 11] the cumulative maximum list should be [10, 10, 10, 10, 10, 11]. Time complexity of constructing a cummax list is O(n) by simply iterating over all the elements and storing the maximum element so far.

The issue is that I want removeFirst operation to be more efficient than simply constructing the cummax list from scratch after it. For example, when removing the first element from the example list, the cummax list should become [7, 8, 8, 8, 11]. After removing another one, it should be [8, 8, 8, 11].

Is it possible to make such a data structure with better time complexity (now it's O(n)) for removing the first element?

We can have a general solution using known "range minimum/maximum query" procedures. For any one element at index j with cumulative maximum first element (on the left) at index i, the value cumulativeMax(j) would be the same as rangeMaximumQuery(i, j).