I can't remember the name of the company, but their is one that provides the ability to do this properly but I don't think it's cheap. Most people do it manually like myself or you can use a plugin like https://vegashero.co/downloads/vegas-hero-plugin/ I insert the demo game into most of our new slot reviews, you will need to have age verification if you provide them to the UK market.
We have tried firstlookgames, but our experience was not good. When you register you get access to all marketing materials but not to the demo links. You have specifically request access to the demo links. Until that point the support was very helpful, fast and friendly. As soon as we requested acces we didn't hear back from anyone even after reaching out multiple times over the course of 2 months. Since we have now realized that we no longer receive any feedback here, we have sent a request to all gaming providers that we know. In the meantime we already have more than 20 gaming providers with a total of over 700 demo games. You can also receive the demo links from casino guru directly on the game page. To embed the games on your website you could do this via iframe. If you are fit in html, css and maybe java script you could easily do this by yourself. Otherwise it may be easier to let someone else write the necessary code for you (fiver is a good place to find someone)
In my opinion, embedding a casino in your website if the casino is not the main task of your site is a bad idea. Think before implementing your plan, and you will understand that the casino is constantly subjected to hacker attacks. There will be quite a lot of people who are not satisfied with your site under such conditions. Now, you can even get professional hacker help, and some people are trying to hire a hacker to hack a casino. Could you think before you do it?