This shouldn’t require multi-zap feature or any other “filtering, path” type of options Zapier offers with premium plans. So, in that case, it should be possible with the “free” version of Zapier.
So whenever you create a new item inside Infinity, you can push it through Zapier and add it as an event in your google calendar.
When it comes to "dates’ basically you will be able to decide which date attribute you want to use when pushing the items to google calendar (through zapier). If you have 2 dats for example, “start date” and “due date”, you can pick only “due date” and the zapier will focus on those.
Here’s where you can check that out: https://zapier.com/apps/infinity/integrations/google-calendar
I’ll be honest, it does take a bit of time to set it all up with Zapier, but besides that - you can try something @micck suggested iCalendar feature and it just might work fine for you!
Hope that helps!