The front squat is a quad builder like nothing else, but if it hurts your wrists you'll be less likely to do it or less likely to add more weight or do more reps.
Some lifters give up on using the proper full grip and resort to the crossed-arms variation, sometimes called the powerlifter's front squat. This method can work, but it's not as stable as the full grip. It's just a Band-Aid.
The problem here often stems from a lack of shoulder and thoracic mobility. Fixing your thoracic mobility keeps the elbows higher and the upper back more upright, taking unwanted pressure off your wrists and lower back. Here's the two-step solution:
1 – Bench T-Spine Mobilization
This allows your lats to stretch out, improving how your shoulder glides on your ribcage. Do 3 sets of 10 with a full breath at the end of the stretch.
2 – Full-Grip Front Rack Holds
It might be more comfortable to just use your fingers on this, but you have to be okay with being uncomfortable.
Put a 25 or 45 pound plate on each side of the bar, grab it as you would for an overhead press, scoop your elbows, and unrack the weight.
Don't breathe into your shoulders so your traps elevate. Instead take a deep breath into your stomach. As you breathe out, feel your traps and neck stretch out. Take 10 breaths, pushing your elbows up as you're able to.
Perform these two drills before your front squat workout to unlock your thoracic spine.