You would need a reliable way to generate an .ics file, which another forum member has done by hosting their own external microservice. When your microservice returns the .ics file, then add it as an attachment in your SendGrid POST. It sounds like this method may be a bit hacky, but it will work.
You could check out a service like AddEvent, if you don’t mind paying for a reliable service. There is also a Github repository that shows you how to generate links that will trigger Google/Apple/Outlook calendar scheduling - I’m guessing that Google/Apple/Microsoft online calendars will have deeplinking that should launch their associated native apps on a mobile device.