Automatically insert table after 1st paragraph in post?

I want to automatically insert a table after the first paragraph of each of my posts.

I see this effect on lots of websites, but I just can’t figure out how they do it. Here are some examples:

https://www.nytimes.com/2008/10/11/opinion/11herbert.html
– note author picture after 1st paragraph

https://musicians.about.com/od/musicindustrybasics/a/demodonts.htm
– note “sponsored links” block

https://news.yahoo.com/s/ap/20081010/ap_on_fe_st/as_odd_cambodia_unique_divorce
– note advertisment after 1st paragraph

I believe this effect is also used in some form in the “Adsense Injection” plugin.

I imagine this might have something to do with search and replace, or perhaps a ‘p:first child’ effect, or (more likely) something I haven’t thought of.

Many thanks – Dave