How would one monetize a one-purpose website?

Let's say I have a few websites like this: http://isitfriday.org/ (this one is not mine though)
Small difference with this one is that mine are created and then get a couple of 10 000 views a day for like a week. (and a bit more effort is put into them) After that the activity goes back down again since the website is only relevant for a small time.
Google ads takes way too long to approve, and they'll never approve a small-content website like that.
Do you guys know of any other ad platform that doesn't require site per site application/validation?

Thanks in advance!

Depends on the use case, but usually one purpose website get returning visitors easier than other sites. For example, there are multitudes of "what is your IP" sites out there, but I always use ipinfo.io. I know the site from a friend and use it ever since even though I never heard of it from google etc.

Useful stuffs just get shared easily. I never spent a dime advertising my free tools/sites and they got constant traffic like a couple thousands viewers per month.

If you need to promote your site, perhaps the easiest way is just share it from a relevant community/social media. If it's useful then people will use it without question.

There is no business model to that site and no point to it.

However, lets say you expanded it to "itsafridaydeal.com"

Now you can post a deal every friday and build a email list you remarket to every friday.