Three fixes I use on rushed mornings: a satin beanie liner, translucent powder at the hairline, and a 20-second cool blast that locks in shape.
Satin under your beanie, not conditioner on your roots

I used to fight hat hair by washing more, conditioning more, adding more leave-in, then wondering why my crown looked flat and my ends looked like a charged balloon. The fix that made the biggest difference had nothing to do with product. It was putting satin between my hair and the hat.
If you wear beanies or baseball caps a lot, the friction is the problem. Wool, acrylic, and even some cotton knits grab at your cuticle all day, then you take the hat off and get that fuzzy halo plus a crushed part line. A satin-lined beanie (or a simple satin bonnet/liner under a regular hat) reduces that drag, so your hair slides instead of snagging. I notice it most at the nape and around my hairline, where baby hairs turn into a weird little fringe the second I step outside.
Two practical notes from doing this through plenty of cold commutes. First, don't size down. A too-tight hat still creates a dent, satin or not. Second, skip the impulse to “pre-fix” hat hair by piling on conditioner at your roots. That just makes the crown collapse faster once it warms up. If you need slip, put a pea-size of a lightweight leave-in (I've used It's a 10 Lite and Ouai Leave In) from mid-length to ends only, then brush it through with something gentle like a Wet Brush. The satin does the rest.
When I take the hat off, I can usually shake out the lengths with my fingers and the shape comes back without that dry-shampoo crunch. And if you're someone who styles your edges or keeps a clean hairline, satin helps you keep that effort intact instead of rubbing it away in two hours.
Set your hairline like makeup: powder where the hat rubs

There's a specific kind of hat hair that isn't about frizz or dents. It's that slightly shiny, separated hairline where your beanie band sits, like your scalp decided to produce oil on schedule the minute you left the house. If you wear any face makeup at all, you already own the fix.
Before the hat goes on, I treat my hairline the way I treat a T-zone. I take a small fluffy brush (an old eyeshadow blending brush works) and tap a translucent setting powder right at the points of contact: temples, just above the ears, and the top edge of the forehead where a beanie tends to press. Laura Mercier Translucent Loose Setting Powder is the classic, but I've also used e.l.f. Halo Glow Setting Powder. The point isn't to make your hair look dusty. You're basically creating a thin, invisible buffer that absorbs sweat and oil before it travels into the hair.
If you have a darker hairline or you hate the idea of translucent powder catching in baby hairs, swap to a tinted pressed powder (MAC Studio Fix Powder Plus Foundation is a reliable one) and use a lighter hand. Tap, don't drag. Dragging is what makes it cling to tiny hairs and look obvious in sunlight.
This is also the one time I'll tell you to use a puff if you have one. Pressing powder in with a puff along the hairline makes it last longer under friction. Think of it like setting concealer, not like “dry shampoo for your face.”
When you take the hat off later, you'll notice your hairline doesn't have that wet-looking band, and you don't have to overcorrect with dry shampoo (which can make the front crunchy and weirdly gray). If you need a quick refresh, a single swipe of the same brush along the hairline is usually enough. It's a tiny grooming move, but it saves the whole look when you're in and out of cold air all day.
The 20-second cool shot that prevents the part dent

Here's the thing nobody tells you when you're racing the clock: if you put a hat on hair that's even a little warm from a blow dry, your part is going to set into whatever shape the hat pushes it into. That's why some mornings you take your beanie off and it looks like your head has a seam.
I fixed this by building in one unglamorous step: a cool shot aimed only at the top of the head, for about 20 seconds. Not a full redo, not a “perfect blowout” situation. Just enough to take the warmth out of the crown and part line so it stops being pliable.
If you're using a hair dryer, finish your normal dry, then flip to cool and focus on two spots: (1) the roots around your part, and (2) the crown, where hats compress the most. Keep the nozzle moving so you're not blasting your scalp. If your dryer has a concentrator nozzle, use it. That directional air is what keeps you from roughing up the cuticle and creating frizz right when you're trying to avoid it.
If you don't have time for a dryer, you can still steal the same effect. Brush the top through, then hold your palms flat on your crown for 10 seconds to pull heat out, like you're cooling a cup of coffee with your hands. It sounds silly. It works.
Two small add-ons from experience: don't apply scalp oils before a hat day (they turn into slip-and-slide + flattening), and if you use a styling cream, keep it off the first inch of roots. I like a light heat protectant spray at the ends (Tresemme Heat Tamer is fine, and cheap) and nothing heavy up top. Once the crown is cool, the hat goes on and your part line stays closer to what you intended, instead of what your beanie decided.