Can keynote pause on the first slide, wait for a trigger, then loop to conclusion?
You can do this inside of Keynote. Right-click on the Animate tab at the top of the right sidebar. You don't need any transition effect so to simplify things I'll use none. Now click on Select All from the Edit menu item. you can see all your slides are selected by looking at the snapshots on the left. Now go back to the right sidebar and where it says Start Transition, pull the menu down and select automatically, and set the delay for the time you want each slide to appear. Now unselect all the slides and click to select 1st one only. Now go back to the right sidebar and for this one slide change the Transition to Automatically with a delay of 600 secs. That's the maximum delay so slide show will start automatically after 10 minutes.
Now you have your animation set up you can click the play button at the top of the Keynote window. This will bring up the 1st slide but it will do nothing until you click. Then it will start displaying all the slides for the number of seconds you entered.  if you need a longer or shorter time for a specific slide, click on that slide in the left sidebar and then in the right sidebar change the Delay Time to a new value.  Now try playing it again.
After you have all the delays set you can also go to Keynote Live at the top of the Keynote window and click that button. This will allow you to issue invitations and then saves the presentation so all you have to do is click on the Green Play button at the top and the presentation will begin.
The 10-minute max delay time was the only way I could get the presentation to stay on slide one for any length of time.  Maybe experimenting with the setting you can find a better way.