Can I use a plugin for a singular page on my website?

What you want is definitely possible.

Although technically it’ll not be just a single event page, rather an event directory. Under that directory there will be single event links created by the event plugin you’ve mentioned. However, those single event links will not have any physical static files, rather those will be managed by WordPress internally.

I understand that you’ve mentioned single page in your question, however, for the use case, it’s most likely that you don’t actually need just a single page, rather a separate directory for WordPress for those events.

So, for example, your site is example.com and you have many custom html & php files in your site. Now you want to create a new page named my-events and want to manage the events using WordPress & The Events Calendar Plugin, in a way that’ll not affect the existing files.

In that case:

1. Create a new directory in your web root named my-events so that it can be reached by example.com/my-events/ URL. (the name of the directory can be anything you want, but to avoid conflict, it should be a new directory that’ll only have WordPress related files)

2. Now you install WordPress in that my-events directory.

3. Delete sample post / page / category etc. created by WordPress by default.

4. Now you install The Event Calendar plugin in your WordPress installation.

5. Create your events.

6. Set events archive page (created by the plugin) as your WordPress Front Page.

That’s it. Now all the static files of your site will work as before & WordPress will serve your events from the example.com/my-events/ directory.

It’s possible to do further customisations, but that’s out of the scope of this answer.