Brimmed hat

 I'm convinced that what I want doesnt exist. I've checked multiple brands so far, and figured I'd ask here.
Looking for a brimmed hat I can wear under my helmet, no button on the top. Preferably merino, if possible, for layering. Definitely not a requirement, but really trying to find something soft vs the mesh trucker cap I'm wearing now.

If you try hard and believe in yourself, any hat is a buttonless hat. I have a few custom DIY ones and they're holding up great without the button.

edit to add: https://www.backcountry.com/smartwool-go-far-feel-good-spokes-5-panel-hat

If you search "5 panel hat," a lot of the options are buttonless. Hope this helps!

If you just want sun protection, try this:

https://bivysack.com/shop/ols/products/helmet-brim

I've also been looking for the holy grail of hats and in the meantime my GF bought my this 686 hat (link below) for $6 from a thrift shop. It's perfect. DWR, no button, drawcord to tighten/loosen and doesnt interfere with helmet. The best part though is that I wanted a structured brim to deflect incoming ice chunks. This one I think will work, but even better, the brim can be turned up so it doesnt limit visibility, but then when hit with a light force (hand, ice, etc.) it easily comes down and then offers the protection I'm looking for.

google "NWT Unisex 686 Sport Hat $30 one size tan DWR nylon flexible bungee slider fit" and itll be an ebay link. MP doesnt allow ebay links.

If you search Google for "cycling under helmet hat" you maybe able to find something that would work.

Maybe this 

https://dabrim.com/

I’ve worn one cycling, and liked it

no button and full sun protection:

https://www.outdoorresearch.com/collections/mens-hats/products/sun-runner-cap-300299

add this if your ears are cold:

https://www.smartwool.com/shop/nts-merino-250-reversible-headband-sw0sc969

Best two I've found:

Warm Weather: Topo Designs Global Hat

Cold Weather: Kavu Fleece Hat

Arcteryx Calidum Hat is great: Granted I got it as a present and $45 is a bit wild to spend on a hat. Im a huge fan of it for touring and trail running

Solomon makes a running hat I’ve been using which is stretchy, no button, firm brim, and a shock cord closure. Fits under a helmet well and the only hat in my entire life that’s fit me (head is 64 cm…) but it seems like it aught to fit normal people too. Got it this summer so I assume they still have it