I have heard that there are some ways to do that , such as with keywords that browsers like Google, etc., will look for when someone does sa search for groups like ours, but I do not know how to go about getting a browser like Google to find those words and make a hit on our group so people will see that we are available.
You've already answered your question :)
depending on your group's name, Google will show it up more
easily.
For example, I have a very specific group and just searching for
"group name groups.io" shows my group just on the first result.
So that's my suggestion. Choose a name that won't leave space for
other results, or at least lots of them, and Google should list
your group as you are wanting to.
By the way,
So far I have removed the ad about my group from my sig because I
don't know whether I can post it here along with my messages. Can
I?