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The process of placing specific data at the beginning of an array involves shifting all the existing elements of the array by one index to the right and inserting the new data at the beginning of the array. This can be achieved through the following steps:

1. Create a new array with the desired size, including space for the new data.
2. Copy all the existing elements of the original array into the new array starting from index 1 (i.e., skipping the first element).
3. Insert the new data at index 0 of the new array.
4. Set the original array to reference the new array.

Alternatively, if the original array has sufficient space at the beginning, the new data can be directly inserted at index 0 by shifting all the existing elements to the right. This can be achieved through a loop that starts from the end of the array and moves each element one index to the right until the desired position is reached.