The Lats are often the culprit of decreased shoulder mobility for many people so ADDRESSING THE EXTENSIBILITY OF THE LATS IS KEY. What is often overlooked, however, is the importance of also gaining range in the TRICEPS. In the front squat position, your elbows are in a FLEXED position, meaning the triceps are maximally lengthened distally, or closer to the elbow. While the triceps still aren't in their fully lengthened position proximally – at the shoulder – in the front squat, someone with restriction in their triceps range may still exhibit limited shoulder flexion range of motion.
So while addressing the lats is key, make sure to also address the triceps. Here is a great way to stretch both the lats and the triceps simultaneously. Using a dowel behind your back, slowly pull down on the dowel until you feel a stretch. With the shoulder in flexion, you are getting a great stretch distally. You can also add some trunk flexion, side bend to the opposite side, and posterior pelvic tilt to further increase the stretch of the lats proximally. Now with the elbow flexed, we are further lengthening the triceps distally (in addition to lengthening the triceps proximally with shoulder flexion).