Usually there’s a plastic clip that bolts to the fender that retains the bumper. That clip may be worn or broken or the clips on the bumper may be broken.
it looks like your fender is bent. I’d pull the bumper and take a look. You may need to just pull the clip straight on the fender side.

 

Did you hit something?

This part of the bumper cover is held in by plastic barbs. I expect they have popped out or if you have received an impact they may have sheared off. Have you tried giving it a firm push to see if the barbs reseat?

If you want a deep dive watch this, it. shows how everything is connected. If you want to take everything apart to see what is really going on you have to remove the plastic trims around the front wheel arches.

 

I didn't hit anything, the owner before me may have.

I've been looking and I cannot find any parts. Do you by chance know where I could find the plastic barbs, the plastic rivets for the liner, and the rivet tool I would need to remove it and put it back on?

When I give it a firm push it just comes back to where it was, so it does not do anything.

Thank you for sending that video, it seems to be extremely helpful.

 

The barbs are molded into the bumper cover so the only way to really fix it if they have snapped off it to replace the bumper cover which would be very expensive. These are not load-bearing. so even if they are damaged you should be to push them back in the slots and be good to go..I did do a write-up on this but I can't find it since the forum software was updated.

I have one of these and it works well, they used to sell big boxes of extra mixed sized rivets for about $5. If not try Amazon. You can by them from dealers or autoparts stores if you want to $5 a rivet

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Don't panic too much, the barbs usually pop out because of minor parking issues or hitting deep snow/sand and can usually be popped back in without having to take everything apart. I just sent you the video so you can see how everything is put together. It looks really serious yet the bumper cover is only a plastic styling cover, after about 15 minutes of work your car will look like something out of a Mad Max movie😀 all the front-end crash protection and structural stuff, sits behind the cover.

 

Don't panic too much, the barbs usually pop out because of minor parking issues or hitting deep snow/sand and can usually be popped back in without having to take everything apart.

So should I try to wiggle / push the bumper back into the slots? And if that does not work, what is the next option?

 

Your right front quarter panel / fender is bent. Its front edge has been been punched rearward and upward which created that wrinkle.

I can see in your first 2 pictures, the wrinkle in the fender’s edge next to the orange side marker light. Given that the bumper cover won’t stay in place when you push on it, I would bet your fender is smacked enough to where the holes for the plastic clips no longer allow the bumper cover to stay where it is supposed to stay. Maybe from previous owner rear-ending another driver or large rock??
My recommendation is remove the plastic bumper cover/fascia. Examine the fender, and you will find you have to pull the leading right front edge forward and downward to get rid of that wrinkle. After you do that, I bet my blue socks you will then have no problem putting the bumper cover back on in the right spot.

 

Your right front quarter panel / fender is bent. Its front edge has been been punched rearward and upward which created that wrinkle.

I can see in your first 2 pictures, the wrinkle in the fender’s edge next to the orange side marker light. Given that the bumper cover won’t stay in place when you push on it, I would bet your fender is smacked enough to where the holes for the plastic clips no longer allow the bumper cover to stay where it is supposed to stay. Maybe from previous owner rear-ending another driver or large rock??
My recommendation is remove the plastic bumper cover/fascia. Examine the fender, and you will find you have to pull the leading right front edge forward and downward to get rid of that wrinkle. After you do that, I bet my blue socks you will then have no problem putting the bumper cover back on in the right spot.

Ya...looks like there's a scratch there too....