If you are on desktop, when clicking the "I am human" checkbox, hold your mouse down for a few seconds, and move it around just a touch for good measure, before letting go. This is usually enough to convince the system you are human and it skips the image hunt.
Look if the site has an option to use the noscript recaptcha (you might be able to force it to appear by blocking scripts). That one's much easier: as long as you get it right it lets you through, and you always have to select three squares (none of that "keep clicking until there's no more matching" garbage).
The first set is all you really need. Answering the second set (if presented) with completely wrong answers will usually cause you to pass. Wild guess -- perhaps ReCAPTCHA is checking for mouse movement and other behavioural heuristics after the initial test.
Have you encountered the CAPTCHA from this monstrosity of a company called Arkose Labs? I don't get angry but I was trying to redeem gift cards for an elderly relative and I was shouting and gave up.
Not sure if I am allowed to paste links but search for "arkose labs reddit" or just the name of this company on Twitter. Or search "arkose labs san francisco" on Google and just read the reviews.
That CAPTCHA on Epic Games Store is hell. Worst part being you have to do it all over again if you fail even once and that one is enough for me to not login.
Easily the worst captcha there is, it makes you do the captcha 10 times (it says 10 to go after you do the first one) and if you get one wrong it doesn't tell you until the end after you've done them all, in which case you have to repeat it.
You can click whatever you want. Every captcha I’ve done in the last year says I missed something, then lets me pass. If I just click on trees and rocks, same thing, it lets me past. I think all they are doing is deeply fingerprinting you and the image matches are a red herring