More often than not, this can be resolved by adopting a stance that has your toes out slightly (slightly!) - play around with different stance widths, and see if there's one which feels friendlier; this is especially relevant when both hips pinch.

Test your hip internal rotation - the bottom of a squat demands your femur (thighbone) to internally rotate in its socket, so if you are missing this movement quality at one or both hips, give these drills a go:

Try a squat that's front-loaded - you may potentially be entering a little too much hip flexion at the bottom of your squat, and this can mess with the movement. Zercher and goblet squats will encourage you to keep your trunk tall.

I would strongly recommend double-checking your hinging form or having somebody look over it - this can often happen if you are rounding your spine, or not initiating the movement by moving your hips back.

Test your hip internal rotation - the bottom of a squat demands your femur (thighbone) to internally rotate in its socket, so if you are missing this movement quality at one or both hips, give these drills a go:

Are you going a bit too low? Ideally when performing most hinge-based movements (Romanian deadlifts, good mornings, etc.), you only want to go until your pelvis runs out of movement range, or until you feel a stretch in your hamstrings and maybe glutes. Remember, the goal is not to hit the floor!

Chances are, you may be initiating the squat in a little too much hip flexion. Try a front-loaded squat such as a Zercher or a goblet squat, see if beginning the movement in a more upright position helps.

Hip flexors and quad tightness - if these two are too shortened, they will be pulling your hips into slight flexion before you've even started the movement. Hit this move:

This could be especially true if the hip pain is only on one side - test the strength of your hip abductors.

Almost for sure something to do with your form - have somebody look over it, and make sure you are rounding your spine, or not initiating the movement by moving your hips back.

Hip flexors and quad tightness - if these two are too shortened, they will be pulling your hips into slight flexion before you've even started the movement. Hit this move:

Deload the hinge - I know it's fun to throw weight around, but we'll never get to the bottom of this unless you can do a perfect, pain-free hinge with just the bar.

Try a single-leg variation - this kickstand hinge is my go-to for most hinge-related problems.