Muscle soreness (or DOMS) is mostly viewed as a good thing. When someone feels DOMS in the days after a training session, they feel that it was productive and that they're doing things right. But is this really the case? Is DOMS a good indicator of muscle growth?
We still don't know for sure what causes DOMS. Is it caused by the actual damage or is it a sign that the damage is being repaired? We're still not sure, but it most likely is related to muscle damage.
Muscle damage consists of tears in the muscle fibers and connective tissue that occur when you train, and it was thought to be one of the main mechanisms of muscle growth, which led us to think that more soreness ➡ more muscle damage ➡ more muscle growth. However, muscle soreness and muscle growth are very poorly correlated. For example, a long-distance run will give you DOMS in the days after. However, you don't grow any muscle from it. Also, there are some body parts where you very rarely experience soreness, but they still respond to training and grow (for me it's the lateral and rear delts).
So no, DOMS is not required for muscle growth. Not only that, too much soreness can even be detrimental. When there's damage, muscle protein synthesis will be directed towards repair instead of hypertrophy, and having very intense DOMS and/or for a lot of days, means a lot of muscle damage. This means that before start growing new muscle, your body has to first repair what was damaged, spending most of its resources and time in that process, and not having much to then build on top of what you already had.
Bottom line, DOMS is not a sign of muscle growth or that you had a good session; it's a natural part of lifting. Don't chase it, but don't be too afraid of it that it stops you from training hard! Lastly, if you have very intense DOMS and/or for a lot of days, consider lowering your training volume and/or intensity for that body part in that day.