First we're going to filter all these new messages and put them under a "G Suite Support" label so you can reference them later if you need.
Gmail uses labels to group your emails into views, just like folders. But unlike folders your emails can have multiple labels which makes it very versatile.
Your Inbox is a view that enables you to see of all current emails. Your Trash folder is another "view" of the emails you sent to trash (deletion). All emails remain in your Gmail until you choose to permanently delete them (empty trash).
OK back to filters, I've done part of the work for you, click this link to open Gmail (and login if you need to):
Once Gmail launches, you will be taken directly into the "create filter" menu, it will look like this:
You will notice that the search bar up the top is also used to create a filter based on your search items. In the background Gmail has already found the first training email (you can see it in the background).
If your screen looks like the one above, then click the Create filter with this search link in the bottom right of the drop-down
Cool! Almost there!
In the next screen we want to apply a label to our emails (this will then put the label on the left-hand side like a folder with all our emails as they arrive).
Check the Apply the Label option and click the drop-down next to it and select New Label to create our first label
Type in your new label name, I'd suggest "G Suite Support"... yeah!
Click Create to make your new label, then finish off your filter by applying to the email already in your inbox (any new ones will get the rule applied automatically)
Your new label will be shown on the left-hand side menu like so:
Oh and see the little blue square? You can colour code your labels too. Just hover over the label and click the little triangle that appears, then select the colour you want... like blue!
Oh, you can also just drag 'n' drop your emails onto labels. Or use the menu item across the top of your inbox to add a label to your email.
Now go forth and create filters and labels for your emails!