The base of any cat introduction is in the following order:
Sound being the only element that we could not control. Hence making our job easier by shifting our effort to only introduce by scent and sight.
Scent is the 1st thing we need to introduce. During this process we have to elimate the element of sight. We do this by using close door or baby gate with cardboard, towel, blanket or etc, covering the baby gate. The mistake i made years ago was to introduce scent without eliminating sight. Hence i have no improvement for months.
With the proper setup done, u can proceed to introduce scent by scent swapping and meal time near the door/gate and slowly make them closer during meal time on both side of the door/gate. The cat will tell you how fast a pace you should go about. When both are comfortable enough, u can open the barrier (towel, blanket, cardboard and etc) to introduce by Sight
With Sight u proceed the same thing such as scent swapping and meal time on both sides. Hence u need to eliminate any free feeding to have a control environment. The idea here is to make both cats see that each other are no threat. Hence u are associating anything possitive like a meal with each other.
If they are having stress at this point u either distance the bowl further during meal time or go back to having a barrier between the door/gate to once again eliminate sight. We have to remember that we are going at a pace that the cat are comfortable at. Slowly u can play with the cats on either side. This once again to associate something positive to sumthing fun and to make each other see that they are a non threat to each other