As i have had a few issues myself with the front squat, here are a few things i have done to help me progress. I love this movement. It is really helping me have a stronger trunk.
Getting into a good rack position isn’t just about wrist flexibility. It also requires good shoulder mobility, thoracic mobility, and flexibility in your lats and triceps, so those areas can always benefit from opening up the range of movement?
When you are working on the clean grip, you can just have your finger tips under the bar; at first even just two will suffice, the index and middle fingers. This helps many lifters with limited wrist flexibility use the clean grip effectively. Remember it is your deltoids that are supporting the bar so brace your upper back and ensure the bar is sitting firmly cushioned on that shelf.
As the weight gets heavier i really have to drive myself up, not just with my legs and butt, but also my elbows and shoulders (so i don’t tip forward). If i do tip forward at all, that puts more pressure on my hands and wrist as i have to use them to keep the bar balanced on my shoulders. A good front squat should be possible with no hands at all in fact. But like you, i like the security of knowing my fingers are underneath it.
One other tip i can suggest, is to reduce the number of reps you do. With front squats, generally the upper back will fatigue before the legs do. If your upper back fatigues then your back will probably cave and the bar will put more pressure on your hands and wrists. Keep reps low (no more than 5 is usually recommended); and if you’re worried about the workout lacking volume, you can increase the number of sets instead. With lower reps, you can continue to get the benefit of improving your front squat form and do it more optimally before fatigue or pain compromises your great work.
I agree with the above. There are lots of things that you could do (some people say wrist curls, some say you can use wrist straps to hold the bar…. etc.), but I personally think that, in most cases (for people who don’t have injuries and generally have good range of motion in their joints) the only and best way to get excellent at something is to train the exact movement more often.
I would add one more thing: you can hold the bar in the rack position for X seconds (I like 60-90 seconds) and just get used to that position. So, get into the power rack, rack the bar in the front rack position, and just stand there and hold it. Either stand or get into the squat position. But then stay still and just maintain the rack position for X seconds. This will help your wrists (and your core!) adjust to the position.